diff --git a/client/client_test.go b/client/client_test.go
index 20846bba..836e4cdb 100644
--- a/client/client_test.go
+++ b/client/client_test.go
@@ -124,6 +124,7 @@ func TestIntegration(t *testing.T) {
 		testLazyImagePush,
 		testStargzLazyPull,
 		testFileOpInputSwap,
+		testRelativeMountpoint,
 	}, mirrors)
 
 	integration.Run(t, []integration.Test{
@@ -3458,6 +3459,44 @@ func testParallelLocalBuilds(t *testing.T, sb integration.Sandbox) {
 	require.NoError(t, err)
 }
 
+// testRelativeMountpoint is a test that relative paths for mountpoints don't
+// fail when runc is upgraded to at least rc95, which introduces an error when
+// mountpoints are not absolute. Relative paths should be transformed to
+// absolute points based on the llb.State's current working directory.
+func testRelativeMountpoint(t *testing.T, sb integration.Sandbox) {
+	requiresLinux(t)
+	c, err := New(context.TODO(), sb.Address())
+	require.NoError(t, err)
+	defer c.Close()
+
+	id := identity.NewID()
+
+	st := llb.Image("busybox:latest").Dir("/root").Run(
+		llb.Shlexf("sh -c 'echo -n %s > /root/relpath/data'", id),
+	).AddMount("relpath", llb.Scratch())
+
+	def, err := st.Marshal(context.TODO())
+	require.NoError(t, err)
+
+	destDir, err := ioutil.TempDir("", "buildkit")
+	require.NoError(t, err)
+	defer os.RemoveAll(destDir)
+
+	_, err = c.Solve(context.TODO(), def, SolveOpt{
+		Exports: []ExportEntry{
+			{
+				Type:      ExporterLocal,
+				OutputDir: destDir,
+			},
+		},
+	}, nil)
+	require.NoError(t, err)
+
+	dt, err := ioutil.ReadFile(filepath.Join(destDir, "data"))
+	require.NoError(t, err)
+	require.Equal(t, dt, []byte(id))
+}
+
 func tmpdir(appliers ...fstest.Applier) (string, error) {
 	tmpdir, err := ioutil.TempDir("", "buildkit-client")
 	if err != nil {
diff --git a/frontend/gateway/container.go b/frontend/gateway/container.go
index e124566d..f234401f 100644
--- a/frontend/gateway/container.go
+++ b/frontend/gateway/container.go
@@ -3,6 +3,7 @@ package gateway
 import (
 	"context"
 	"fmt"
+	"path/filepath"
 	"runtime"
 	"sort"
 	"strings"
@@ -75,7 +76,7 @@ func NewContainer(ctx context.Context, w worker.Worker, sm *session.Manager, g s
 
 	name := fmt.Sprintf("container %s", req.ContainerID)
 	mm := mounts.NewMountManager(name, w.CacheManager(), sm, w.MetadataStore())
-	p, err := PrepareMounts(ctx, mm, w.CacheManager(), g, mnts, refs, func(m *opspb.Mount, ref cache.ImmutableRef) (cache.MutableRef, error) {
+	p, err := PrepareMounts(ctx, mm, w.CacheManager(), g, "", mnts, refs, func(m *opspb.Mount, ref cache.ImmutableRef) (cache.MutableRef, error) {
 		cm := w.CacheManager()
 		if m.Input != opspb.Empty {
 			cm = refs[m.Input].Worker.CacheManager()
@@ -132,7 +133,7 @@ type MountMutableRef struct {
 
 type MakeMutable func(m *opspb.Mount, ref cache.ImmutableRef) (cache.MutableRef, error)
 
-func PrepareMounts(ctx context.Context, mm *mounts.MountManager, cm cache.Manager, g session.Group, mnts []*opspb.Mount, refs []*worker.WorkerRef, makeMutable MakeMutable) (p PreparedMounts, err error) {
+func PrepareMounts(ctx context.Context, mm *mounts.MountManager, cm cache.Manager, g session.Group, cwd string, mnts []*opspb.Mount, refs []*worker.WorkerRef, makeMutable MakeMutable) (p PreparedMounts, err error) {
 	// loop over all mounts, fill in mounts, root and outputs
 	for i, m := range mnts {
 		var (
@@ -254,7 +255,11 @@ func PrepareMounts(ctx context.Context, mm *mounts.MountManager, cm cache.Manage
 			p.Root = mountWithSession(root, g)
 		} else {
 			mws := mountWithSession(mountable, g)
-			mws.Dest = m.Dest
+			dest := m.Dest
+			if !filepath.IsAbs(filepath.Clean(dest)) {
+				dest = filepath.Join("/", cwd, dest)
+			}
+			mws.Dest = dest
 			mws.Readonly = m.Readonly
 			mws.Selector = m.Selector
 			p.Mounts = append(p.Mounts, mws)
diff --git a/solver/llbsolver/ops/exec.go b/solver/llbsolver/ops/exec.go
index b5ef0f16..1e0b7ad9 100644
--- a/solver/llbsolver/ops/exec.go
+++ b/solver/llbsolver/ops/exec.go
@@ -243,7 +243,7 @@ func (e *execOp) Exec(ctx context.Context, g session.Group, inputs []solver.Resu
 		}
 	}
 
-	p, err := gateway.PrepareMounts(ctx, e.mm, e.cm, g, e.op.Mounts, refs, func(m *pb.Mount, ref cache.ImmutableRef) (cache.MutableRef, error) {
+	p, err := gateway.PrepareMounts(ctx, e.mm, e.cm, g, e.op.Meta.Cwd, e.op.Mounts, refs, func(m *pb.Mount, ref cache.ImmutableRef) (cache.MutableRef, error) {
 		desc := fmt.Sprintf("mount %s from exec %s", m.Dest, strings.Join(e.op.Meta.Args, " "))
 		return e.cm.New(ctx, ref, g, cache.WithDescription(desc))
 	})