diff --git a/sdk/trace/provider.go b/sdk/trace/provider.go
index 4c6e6e2ecf0..901e8d4a76d 100644
--- a/sdk/trace/provider.go
+++ b/sdk/trace/provider.go
@@ -144,7 +144,9 @@ func (p *TracerProvider) UnregisterSpanProcessor(s SpanProcessor) {
 	}
 	if stopOnce != nil {
 		stopOnce.state.Do(func() {
-			otel.Handle(s.Shutdown(context.Background()))
+			if err := s.Shutdown(context.Background()); err != nil {
+				otel.Handle(err)
+			}
 		})
 	}
 	if len(new) > 1 {
@@ -192,7 +194,9 @@ func (p *TracerProvider) Shutdown(ctx context.Context) error {
 
 	for _, sps := range spss {
 		sps.state.Do(func() {
-			otel.Handle(sps.sp.Shutdown(ctx))
+			if err := sps.sp.Shutdown(ctx); err != nil {
+				otel.Handle(err)
+			}
 		})
 	}
 	return nil
diff --git a/sdk/trace/provider_test.go b/sdk/trace/provider_test.go
index ea0a2f870d5..32bec2fb75c 100644
--- a/sdk/trace/provider_test.go
+++ b/sdk/trace/provider_test.go
@@ -16,16 +16,20 @@ package trace
 
 import (
 	"context"
+	"errors"
 	"testing"
+
+	"github.com/stretchr/testify/assert"
 )
 
 type basicSpanProcesor struct {
-	running bool
+	running             bool
+	injectShutdownError error
 }
 
 func (t *basicSpanProcesor) Shutdown(context.Context) error {
 	t.running = false
-	return nil
+	return t.injectShutdownError
 }
 
 func (t *basicSpanProcesor) OnStart(parent context.Context, s ReadWriteSpan) {}
@@ -45,3 +49,36 @@ func TestShutdownTraceProvider(t *testing.T) {
 		t.Errorf("Error shutdown basicSpanProcesor\n")
 	}
 }
+
+func TestFailedProcessorShutdown(t *testing.T) {
+	handler.Reset()
+	stp := NewTracerProvider()
+	spErr := errors.New("basic span processor shutdown failure")
+	sp := &basicSpanProcesor{
+		running:             true,
+		injectShutdownError: spErr,
+	}
+	stp.RegisterSpanProcessor(sp)
+
+	_ = stp.Shutdown(context.Background())
+
+	assert.Contains(t, handler.errs, spErr)
+}
+
+func TestFailedProcessorShutdownInUnregister(t *testing.T) {
+	handler.Reset()
+	stp := NewTracerProvider()
+	spErr := errors.New("basic span processor shutdown failure")
+	sp := &basicSpanProcesor{
+		running:             true,
+		injectShutdownError: spErr,
+	}
+	stp.RegisterSpanProcessor(sp)
+	stp.UnregisterSpanProcessor(sp)
+
+	assert.Contains(t, handler.errs, spErr)
+
+	handler.errs = nil
+	_ = stp.Shutdown(context.Background())
+	assert.Empty(t, handler.errs)
+}
diff --git a/sdk/trace/trace_test.go b/sdk/trace/trace_test.go
index 462978f8181..22ff6b20fb9 100644
--- a/sdk/trace/trace_test.go
+++ b/sdk/trace/trace_test.go
@@ -41,20 +41,30 @@ import (
 	"go.opentelemetry.io/otel/sdk/resource"
 )
 
+type storingHandler struct {
+	errs []error
+}
+
+func (s *storingHandler) Handle(err error) {
+	s.errs = append(s.errs, err)
+}
+
+func (s *storingHandler) Reset() {
+	s.errs = nil
+}
+
 var (
 	tid trace.TraceID
 	sid trace.SpanID
-)
 
-type discardHandler struct{}
-
-func (*discardHandler) Handle(_ error) {}
+	handler *storingHandler = &storingHandler{}
+)
 
 func init() {
 	tid, _ = trace.TraceIDFromHex("01020304050607080102040810203040")
 	sid, _ = trace.SpanIDFromHex("0102040810203040")
 
-	otel.SetErrorHandler(new(discardHandler))
+	otel.SetErrorHandler(handler)
 }
 
 func TestTracerFollowsExpectedAPIBehaviour(t *testing.T) {