diff --git a/Dockerfile b/Dockerfile
index 27adf06..9b3c852 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -51,6 +51,7 @@
 RUN go install github.com/bradfitz/gomemcache/memcache
 RUN go install golang.org/x/tools/godoc/static
 RUN go install golang.org/x/tools/imports
+RUN go install github.com/rogpeppe/go-internal/modfile
 RUN go install github.com/rogpeppe/go-internal/txtar
 
 # Add and compile playground daemon
diff --git a/fmt.go b/fmt.go
index c5aa943..002bd34 100644
--- a/fmt.go
+++ b/fmt.go
@@ -9,8 +9,9 @@
 	"fmt"
 	"go/format"
 	"net/http"
-	"strings"
+	"path"
 
+	"github.com/rogpeppe/go-internal/modfile"
 	"golang.org/x/tools/imports"
 )
 
@@ -30,30 +31,46 @@
 
 	fixImports := r.FormValue("imports") != ""
 	for _, f := range fs.files {
-		if !strings.HasSuffix(f, ".go") {
-			continue
-		}
-		var out []byte
-		var err error
-		in := fs.m[f]
-		if fixImports {
-			// TODO: pass options to imports.Process so it
-			// can find symbols in sibling files.
-			out, err = imports.Process(progName, in, nil)
-		} else {
-			out, err = format.Source(in)
-		}
-		if err != nil {
-			errMsg := err.Error()
-			// Prefix the error returned by format.Source.
-			if !strings.HasPrefix(errMsg, f) {
-				errMsg = fmt.Sprintf("%v:%v", f, errMsg)
+		switch {
+		case path.Ext(f) == ".go":
+			var out []byte
+			var err error
+			in := fs.Data(f)
+			if fixImports {
+				// TODO: pass options to imports.Process so it
+				// can find symbols in sibling files.
+				out, err = imports.Process(f, in, nil)
+			} else {
+				out, err = format.Source(in)
 			}
-			json.NewEncoder(w).Encode(fmtResponse{Error: errMsg})
-			return
+			if err != nil {
+				errMsg := err.Error()
+				if !fixImports {
+					// Unlike imports.Process, format.Source does not prefix
+					// the error with the file path. So, do it ourselves here.
+					errMsg = fmt.Sprintf("%v:%v", f, errMsg)
+				}
+				json.NewEncoder(w).Encode(fmtResponse{Error: errMsg})
+				return
+			}
+			fs.AddFile(f, out)
+		case path.Base(f) == "go.mod":
+			out, err := formatGoMod(f, fs.Data(f))
+			if err != nil {
+				json.NewEncoder(w).Encode(fmtResponse{Error: err.Error()})
+				return
+			}
+			fs.AddFile(f, out)
 		}
-		fs.AddFile(f, out)
 	}
 
 	json.NewEncoder(w).Encode(fmtResponse{Body: string(fs.Format())})
 }
+
+func formatGoMod(file string, data []byte) ([]byte, error) {
+	f, err := modfile.Parse(file, data, nil)
+	if err != nil {
+		return nil, err
+	}
+	return f.Format()
+}
diff --git a/fmt_test.go b/fmt_test.go
index b8a1b9a..e601dc3 100644
--- a/fmt_test.go
+++ b/fmt_test.go
@@ -47,9 +47,53 @@
 			want: "package main\n-- two.go --\npackage main\n\nvar X = 5\n",
 		},
 		{
-			name: "only_format_go",
-			body: "    package main\n\n\n-- go.mod --\n   module foo\n",
-			want: "package main\n-- go.mod --\n   module foo\n",
+			name: "single_go.mod_with_header",
+			body: "-- go.mod --\n   module   \"foo\"   ",
+			want: "-- go.mod --\nmodule foo\n",
+		},
+		{
+			name: "multi_go.mod_with_header",
+			body: "-- a/go.mod --\n  module foo\n\n\n-- b/go.mod --\n   module  \"bar\"",
+			want: "-- a/go.mod --\nmodule foo\n-- b/go.mod --\nmodule bar\n",
+		},
+		{
+			name: "only_format_go_and_go.mod",
+			body: "    package   main   \n\n\n" +
+				"-- go.mod --\n   module   foo   \n\n\n" +
+				"-- plain.txt --\n   plain   text   \n\n\n",
+			want: "package main\n-- go.mod --\nmodule foo\n-- plain.txt --\n   plain   text   \n\n\n",
+		},
+		{
+			name:    "error_gofmt",
+			body:    "package 123\n",
+			wantErr: "prog.go:1:9: expected 'IDENT', found 123",
+		},
+		{
+			name:    "error_gofmt_with_header",
+			body:    "-- dir/one.go --\npackage 123\n",
+			wantErr: "dir/one.go:1:9: expected 'IDENT', found 123",
+		},
+		{
+			name:    "error_goimports",
+			body:    "package 123\n",
+			imports: true,
+			wantErr: "prog.go:1:9: expected 'IDENT', found 123",
+		},
+		{
+			name:    "error_goimports_with_header",
+			body:    "-- dir/one.go --\npackage 123\n",
+			imports: true,
+			wantErr: "dir/one.go:1:9: expected 'IDENT', found 123",
+		},
+		{
+			name:    "error_go.mod",
+			body:    "-- go.mod --\n123\n",
+			wantErr: "go.mod:1: unknown directive: 123",
+		},
+		{
+			name:    "error_go.mod_with_header",
+			body:    "-- dir/go.mod --\n123\n",
+			wantErr: "dir/go.mod:1: unknown directive: 123",
 		},
 	} {
 		t.Run(tt.name, func(t *testing.T) {
diff --git a/txtar_test.go b/txtar_test.go
index ae1ef96..493d140 100644
--- a/txtar_test.go
+++ b/txtar_test.go
@@ -147,7 +147,7 @@
 		if i == 0 && f == progName && fs.noHeader {
 			implicit = " (implicit)"
 		}
-		fmt.Fprintf(&sb, "[file %q%s]: %q\n", f, implicit, fs.m[f])
+		fmt.Fprintf(&sb, "[file %q%s]: %q\n", f, implicit, fs.Data(f))
 	}
 	return sb.String()
 }