diff --git a/src/debug/elf/file.go b/src/debug/elf/file.go
index b2adc2834fc496..f92a2b00525385 100644
--- a/src/debug/elf/file.go
+++ b/src/debug/elf/file.go
@@ -276,7 +276,6 @@ func NewFile(r io.ReaderAt) (*File, error) {
 	var phentsize, phnum int
 	var shoff int64
 	var shentsize, shnum, shstrndx int
-	shstrndx = -1
 	switch f.Class {
 	case ELFCLASS32:
 		hdr := new(Header32)
@@ -318,7 +317,11 @@ func NewFile(r io.ReaderAt) (*File, error) {
 		shstrndx = int(hdr.Shstrndx)
 	}
 
-	if shnum > 0 && shoff > 0 && (shstrndx < 0 || shstrndx >= shnum) {
+	if shoff == 0 && shnum != 0 {
+		return nil, &FormatError{0, "invalid ELF shnum for shoff=0", shnum}
+	}
+
+	if shnum > 0 && shstrndx >= shnum {
 		return nil, &FormatError{0, "invalid ELF shstrndx", shstrndx}
 	}
 
diff --git a/src/debug/elf/file_test.go b/src/debug/elf/file_test.go
index d7c1e9f800d862..b826a0ff050e25 100644
--- a/src/debug/elf/file_test.go
+++ b/src/debug/elf/file_test.go
@@ -810,3 +810,14 @@ func TestNoSectionOverlaps(t *testing.T) {
 		}
 	}
 }
+
+func TestIssue10996(t *testing.T) {
+	data := []byte("\u007fELF\x02\x01\x010000000000000" +
+		"\x010000000000000000000" +
+		"\x00\x00\x00\x00\x00\x00\x00\x0000000000\x00\x00\x00\x00" +
+		"0000")
+	_, err := NewFile(bytes.NewReader(data))
+	if err == nil {
+		t.Fatalf("opening invalid ELF file unexpectedly suceeded")
+	}
+}