diff --git a/onnxruntime_go.go b/onnxruntime_go.go
index 2e2acfe..fb6666a 100644
--- a/onnxruntime_go.go
+++ b/onnxruntime_go.go
@@ -28,6 +28,23 @@ var ortMemoryInfo *C.OrtMemoryInfo
 var NotInitializedError error = fmt.Errorf("InitializeRuntime() has either " +
 	"not yet been called, or did not return successfully")
 
+var ZeroShapeLengthError error = fmt.Errorf("The shape has no dimensions")
+
+var ShapeOverflowError error = fmt.Errorf("The shape's flattened size " +
+	"overflows an int64")
+
+// This type of error is returned when we attempt to validate a tensor that has
+// a negative or 0 dimension.
+type BadShapeDimensionError struct {
+	DimensionIndex int
+	DimensionSize  int64
+}
+
+func (e *BadShapeDimensionError) Error() string {
+	return fmt.Sprintf("Dimension %d of the shape has invalid value %d",
+		e.DimensionIndex, e.DimensionSize)
+}
+
 // Does two things: converts the given OrtStatus to a Go error, and releases
 // the status. If the status is nil, this does nothing and returns nil.
 func statusToError(status *C.OrtStatus) error {
@@ -121,7 +138,10 @@ func NewShape(dimensions ...int64) Shape {
 	return Shape(dimensions)
 }
 
-// Returns the total number of elements in a tensor with the given shape.
+// Returns the total number of elements in a tensor with the given shape. Note
+// that this may be an invalid value due to overflow or negative dimensions. If
+// a shape comes from an untrusted source, it may be a good practice to call
+// Validate() prior to trusting the FlattenedSize.
 func (s Shape) FlattenedSize() int64 {
 	if len(s) == 0 {
 		return 0
@@ -133,6 +153,38 @@ func (s Shape) FlattenedSize() int64 {
 	return toReturn
 }
 
+// Returns a non-nil error if the shape has bad or zero dimensions. May return
+// a ZeroShapeLengthError, a ShapeOverflowError, or an BadShapeDimensionError.
+// In the future, this may return other types of errors if it others become
+// necessary.
+func (s Shape) Validate() error {
+	if len(s) == 0 {
+		return ZeroShapeLengthError
+	}
+	if s[0] <= 0 {
+		return &BadShapeDimensionError{
+			DimensionIndex: 0,
+			DimensionSize:  s[0],
+		}
+	}
+	flattenedSize := int64(s[0])
+	for i := 1; i < len(s); i++ {
+		d := s[i]
+		if d <= 0 {
+			return &BadShapeDimensionError{
+				DimensionIndex: i,
+				DimensionSize:  d,
+			}
+		}
+		tmp := flattenedSize * d
+		if tmp < flattenedSize {
+			return ShapeOverflowError
+		}
+		flattenedSize = tmp
+	}
+	return nil
+}
+
 // Makes and returns a deep copy of the Shape.
 func (s Shape) Clone() Shape {
 	toReturn := make([]int64, len(s))
@@ -205,10 +257,11 @@ func (t *Tensor[T]) Clone() (*Tensor[T], error) {
 // Creates a new empty tensor with the given shape. The shape provided to this
 // function is copied, and is no longer needed after this function returns.
 func NewEmptyTensor[T TensorData](s Shape) (*Tensor[T], error) {
-	elementCount := s.FlattenedSize()
-	if elementCount == 0 {
-		return nil, fmt.Errorf("Got invalid shape containing 0 elements")
+	e := s.Validate()
+	if e != nil {
+		return nil, fmt.Errorf("Invalid tensor shape: %w", e)
 	}
+	elementCount := s.FlattenedSize()
 	data := make([]T, elementCount)
 	return NewTensor(s, data)
 }
@@ -221,7 +274,10 @@ func NewTensor[T TensorData](s Shape, data []T) (*Tensor[T], error) {
 	if !IsInitialized() {
 		return nil, NotInitializedError
 	}
-
+	e := s.Validate()
+	if e != nil {
+		return nil, fmt.Errorf("Invalid tensor shape: %w", e)
+	}
 	elementCount := s.FlattenedSize()
 	if elementCount > int64(len(data)) {
 		return nil, fmt.Errorf("The tensor's shape (%s) requires %d "+
diff --git a/onnxruntime_test.go b/onnxruntime_test.go
index 474df99..804e1a9 100644
--- a/onnxruntime_test.go
+++ b/onnxruntime_test.go
@@ -136,6 +136,56 @@ func TestCreateTensor(t *testing.T) {
 	}
 }
 
+func TestBadTensorShapes(t *testing.T) {
+	InitializeRuntime(t)
+	defer DestroyEnvironment()
+	s := NewShape()
+	_, e := NewEmptyTensor[float64](s)
+	if e == nil {
+		t.Logf("Didn't get an error when creating a tensor with an empty " +
+			"shape.\n")
+		t.FailNow()
+	}
+	t.Logf("Got expected error when creating a tensor with an empty shape: "+
+		"%s\n", e)
+	s = NewShape(10, 0, 10)
+	_, e = NewEmptyTensor[uint16](s)
+	if e == nil {
+		t.Logf("Didn't get an error when creating a tensor with a shape " +
+			"containing a 0 dimension.\n")
+		t.FailNow()
+	}
+	t.Logf("Got expected error when creating a tensor with a 0 dimension: "+
+		"%s\n", e)
+	s = NewShape(10, 10, -10)
+	_, e = NewEmptyTensor[int32](s)
+	if e == nil {
+		t.Logf("Didn't get an error when creating a tensor with a negative " +
+			"dimension.\n")
+		t.FailNow()
+	}
+	t.Logf("Got expected error when creating a tensor with a negative "+
+		"dimension: %s\n", e)
+	s = NewShape(10, -10, -10)
+	_, e = NewEmptyTensor[uint64](s)
+	if e == nil {
+		t.Logf("Didn't get an error when creating a tensor with two " +
+			"negative dimensions.\n")
+		t.FailNow()
+	}
+	t.Logf("Got expected error when creating a tensor with two negative "+
+		"dimensions: %s\n", e)
+	s = NewShape(int64(1)<<62, 1, int64(1)<<62)
+	_, e = NewEmptyTensor[float32](s)
+	if e == nil {
+		t.Logf("Didn't get an error when creating a tensor with an " +
+			"overflowing shape.\n")
+		t.FailNow()
+	}
+	t.Logf("Got expected error when creating a tensor with an overflowing "+
+		"shape: %s\n", e)
+}
+
 func TestCloneTensor(t *testing.T) {
 	InitializeRuntime(t)
 	originalData := []float32{1, 2, 3, 4}