diff --git a/fastapi/dependencies/utils.py b/fastapi/dependencies/utils.py
index 28c57c296..c898ab7db 100644
--- a/fastapi/dependencies/utils.py
+++ b/fastapi/dependencies/utils.py
@@ -131,12 +131,17 @@ def get_flat_dependant(dependant: Dependant) -> Dependant:
 
 
 def is_scalar_field(field: Field) -> bool:
-    return (
+    if not (
         field.shape == Shape.SINGLETON
         and not lenient_issubclass(field.type_, BaseModel)
         and not lenient_issubclass(field.type_, sequence_types + (dict,))
         and not isinstance(field.schema, params.Body)
-    )
+    ):
+        return False
+    if field.sub_fields:
+        if not all(is_scalar_field(f) for f in field.sub_fields):
+            return False
+    return True
 
 
 def is_scalar_sequence_field(field: Field) -> bool:
diff --git a/tests/test_union_body.py b/tests/test_union_body.py
new file mode 100644
index 000000000..b7b8b38b2
--- /dev/null
+++ b/tests/test_union_body.py
@@ -0,0 +1,124 @@
+from typing import Optional, Union
+
+from fastapi import FastAPI
+from pydantic import BaseModel
+from starlette.testclient import TestClient
+
+app = FastAPI()
+
+
+class Item(BaseModel):
+    name: Optional[str] = None
+
+
+class OtherItem(BaseModel):
+    price: int
+
+
+@app.post("/items/")
+def save_union_body(item: Union[OtherItem, Item]):
+    return {"item": item}
+
+
+client = TestClient(app)
+
+item_openapi_schema = {
+    "openapi": "3.0.2",
+    "info": {"title": "Fast API", "version": "0.1.0"},
+    "paths": {
+        "/items/": {
+            "post": {
+                "responses": {
+                    "200": {
+                        "description": "Successful Response",
+                        "content": {"application/json": {"schema": {}}},
+                    },
+                    "422": {
+                        "description": "Validation Error",
+                        "content": {
+                            "application/json": {
+                                "schema": {
+                                    "$ref": "#/components/schemas/HTTPValidationError"
+                                }
+                            }
+                        },
+                    },
+                },
+                "summary": "Save Union Body",
+                "operationId": "save_union_body_items__post",
+                "requestBody": {
+                    "content": {
+                        "application/json": {
+                            "schema": {
+                                "title": "Item",
+                                "anyOf": [
+                                    {"$ref": "#/components/schemas/OtherItem"},
+                                    {"$ref": "#/components/schemas/Item"},
+                                ],
+                            }
+                        }
+                    },
+                    "required": True,
+                },
+            }
+        }
+    },
+    "components": {
+        "schemas": {
+            "OtherItem": {
+                "title": "OtherItem",
+                "required": ["price"],
+                "type": "object",
+                "properties": {"price": {"title": "Price", "type": "integer"}},
+            },
+            "Item": {
+                "title": "Item",
+                "type": "object",
+                "properties": {"name": {"title": "Name", "type": "string"}},
+            },
+            "ValidationError": {
+                "title": "ValidationError",
+                "required": ["loc", "msg", "type"],
+                "type": "object",
+                "properties": {
+                    "loc": {
+                        "title": "Location",
+                        "type": "array",
+                        "items": {"type": "string"},
+                    },
+                    "msg": {"title": "Message", "type": "string"},
+                    "type": {"title": "Error Type", "type": "string"},
+                },
+            },
+            "HTTPValidationError": {
+                "title": "HTTPValidationError",
+                "type": "object",
+                "properties": {
+                    "detail": {
+                        "title": "Detail",
+                        "type": "array",
+                        "items": {"$ref": "#/components/schemas/ValidationError"},
+                    }
+                },
+            },
+        }
+    },
+}
+
+
+def test_item_openapi_schema():
+    response = client.get("/openapi.json")
+    assert response.status_code == 200
+    assert response.json() == item_openapi_schema
+
+
+def test_post_other_item():
+    response = client.post("/items/", json={"price": 100})
+    assert response.status_code == 200
+    assert response.json() == {"item": {"price": 100}}
+
+
+def test_post_item():
+    response = client.post("/items/", json={"name": "Foo"})
+    assert response.status_code == 200
+    assert response.json() == {"item": {"name": "Foo"}}
diff --git a/tests/test_union_inherited_body.py b/tests/test_union_inherited_body.py
new file mode 100644
index 000000000..022326e51
--- /dev/null
+++ b/tests/test_union_inherited_body.py
@@ -0,0 +1,140 @@
+import sys
+from typing import Optional, Union
+
+import pytest
+from fastapi import FastAPI
+from pydantic import BaseModel
+from starlette.testclient import TestClient
+
+# In Python 3.6:
+# u = Union[ExtendedItem, Item] == __main__.Item
+
+# But in Python 3.7:
+# u = Union[ExtendedItem, Item] == typing.Union[__main__.ExtendedItem, __main__.Item]
+skip_py36 = pytest.mark.skipif(sys.version_info < (3, 7), reason="skip python3.6")
+
+app = FastAPI()
+
+
+class Item(BaseModel):
+    name: Optional[str] = None
+
+
+class ExtendedItem(Item):
+    age: int
+
+
+@app.post("/items/")
+def save_union_different_body(item: Union[ExtendedItem, Item]):
+    return {"item": item}
+
+
+client = TestClient(app)
+
+
+inherited_item_openapi_schema = {
+    "openapi": "3.0.2",
+    "info": {"title": "Fast API", "version": "0.1.0"},
+    "paths": {
+        "/items/": {
+            "post": {
+                "responses": {
+                    "200": {
+                        "description": "Successful Response",
+                        "content": {"application/json": {"schema": {}}},
+                    },
+                    "422": {
+                        "description": "Validation Error",
+                        "content": {
+                            "application/json": {
+                                "schema": {
+                                    "$ref": "#/components/schemas/HTTPValidationError"
+                                }
+                            }
+                        },
+                    },
+                },
+                "summary": "Save Union Different Body",
+                "operationId": "save_union_different_body_items__post",
+                "requestBody": {
+                    "content": {
+                        "application/json": {
+                            "schema": {
+                                "title": "Item",
+                                "anyOf": [
+                                    {"$ref": "#/components/schemas/ExtendedItem"},
+                                    {"$ref": "#/components/schemas/Item"},
+                                ],
+                            }
+                        }
+                    },
+                    "required": True,
+                },
+            }
+        }
+    },
+    "components": {
+        "schemas": {
+            "Item": {
+                "title": "Item",
+                "type": "object",
+                "properties": {"name": {"title": "Name", "type": "string"}},
+            },
+            "ExtendedItem": {
+                "title": "ExtendedItem",
+                "required": ["age"],
+                "type": "object",
+                "properties": {
+                    "name": {"title": "Name", "type": "string"},
+                    "age": {"title": "Age", "type": "integer"},
+                },
+            },
+            "ValidationError": {
+                "title": "ValidationError",
+                "required": ["loc", "msg", "type"],
+                "type": "object",
+                "properties": {
+                    "loc": {
+                        "title": "Location",
+                        "type": "array",
+                        "items": {"type": "string"},
+                    },
+                    "msg": {"title": "Message", "type": "string"},
+                    "type": {"title": "Error Type", "type": "string"},
+                },
+            },
+            "HTTPValidationError": {
+                "title": "HTTPValidationError",
+                "type": "object",
+                "properties": {
+                    "detail": {
+                        "title": "Detail",
+                        "type": "array",
+                        "items": {"$ref": "#/components/schemas/ValidationError"},
+                    }
+                },
+            },
+        }
+    },
+}
+
+
+@skip_py36
+def test_inherited_item_openapi_schema():
+    response = client.get("/openapi.json")
+    assert response.status_code == 200
+    assert response.json() == inherited_item_openapi_schema
+
+
+@skip_py36
+def test_post_extended_item():
+    response = client.post("/items/", json={"name": "Foo", "age": 5})
+    assert response.status_code == 200
+    assert response.json() == {"item": {"name": "Foo", "age": 5}}
+
+
+@skip_py36
+def test_post_item():
+    response = client.post("/items/", json={"name": "Foo"})
+    assert response.status_code == 200
+    assert response.json() == {"item": {"name": "Foo"}}