diff --git a/container/id/id.go b/container/id/id.go
index 569968a..1cbd60b 100644
--- a/container/id/id.go
+++ b/container/id/id.go
@@ -3,6 +3,7 @@ package cid
 import (
 	"crypto/sha256"
 	"fmt"
+	"strings"
 
 	"git.frostfs.info/TrueCloudLab/frostfs-sdk-go/api/refs"
 	"github.com/mr-tron/base58"
@@ -113,3 +114,9 @@ func (id *ID) DecodeString(s string) error {
 func (id ID) String() string {
 	return id.EncodeToString()
 }
+
+// Cmp returns an integer comparing two base58 encoded container ID lexicographically.
+// The result will be 0 if id1 == id2, -1 if id1 < id2, and +1 if id1 > id2.
+func (id ID) Cmp(id2 ID) int {
+	return strings.Compare(id.EncodeToString(), id2.EncodeToString())
+}
diff --git a/container/id/id_test.go b/container/id/id_test.go
index 6f60d92..2bbd8b3 100644
--- a/container/id/id_test.go
+++ b/container/id/id_test.go
@@ -3,6 +3,8 @@ package cid_test
 import (
 	"crypto/rand"
 	"crypto/sha256"
+	"slices"
+	"strings"
 	"testing"
 
 	"git.frostfs.info/TrueCloudLab/frostfs-sdk-go/api/refs"
@@ -106,3 +108,17 @@ func TestID_Encode(t *testing.T) {
 		require.Equal(t, emptyID, id.EncodeToString())
 	})
 }
+
+func TestID_Cmp(t *testing.T) {
+	var arr []cid.ID
+	for i := 0; i < 3; i++ {
+		checksum := randSHA256Checksum()
+		arr = append(arr, cidtest.IDWithChecksum(checksum))
+	}
+
+	slices.SortFunc(arr, cid.ID.Cmp)
+
+	for i := 1; i < len(arr); i++ {
+		require.NotEqual(t, strings.Compare(arr[i-1].EncodeToString(), arr[i].EncodeToString()), 1, "array is not sorted correctly")
+	}
+}
diff --git a/object/id/id.go b/object/id/id.go
index d1dfe80..29e6a3a 100644
--- a/object/id/id.go
+++ b/object/id/id.go
@@ -4,6 +4,7 @@ import (
 	"crypto/ecdsa"
 	"crypto/sha256"
 	"fmt"
+	"strings"
 
 	"git.frostfs.info/TrueCloudLab/frostfs-sdk-go/api/refs"
 	frostfscrypto "git.frostfs.info/TrueCloudLab/frostfs-sdk-go/crypto"
@@ -167,3 +168,9 @@ func (id *ID) UnmarshalJSON(data []byte) error {
 
 	return nil
 }
+
+// Cmp returns an integer comparing two base58 encoded object ID lexicographically.
+// The result will be 0 if id1 == id2, -1 if id1 < id2, and +1 if id1 > id2.
+func (id ID) Cmp(id2 ID) int {
+	return strings.Compare(id.EncodeToString(), id2.EncodeToString())
+}
diff --git a/object/id/id_test.go b/object/id/id_test.go
index e1a2e26..9df6186 100644
--- a/object/id/id_test.go
+++ b/object/id/id_test.go
@@ -3,7 +3,9 @@ package oid
 import (
 	"crypto/rand"
 	"crypto/sha256"
+	"slices"
 	"strconv"
+	"strings"
 	"testing"
 
 	"git.frostfs.info/TrueCloudLab/frostfs-sdk-go/api/refs"
@@ -180,3 +182,16 @@ func TestID_Encode(t *testing.T) {
 		require.Equal(t, emptyID, id.EncodeToString())
 	})
 }
+
+func TestID_Cmp(t *testing.T) {
+	id1 := randID(t)
+	id2 := randID(t)
+	id3 := randID(t)
+
+	arr := []ID{id1, id2, id3}
+
+	slices.SortFunc(arr, ID.Cmp)
+	for i := 1; i < len(arr); i++ {
+		require.NotEqual(t, strings.Compare(arr[i-1].EncodeToString(), arr[i].EncodeToString()), 1, "array is not sorted correctly")
+	}
+}
diff --git a/user/id.go b/user/id.go
index c8e2d14..c77ae67 100644
--- a/user/id.go
+++ b/user/id.go
@@ -4,6 +4,7 @@ import (
 	"bytes"
 	"errors"
 	"fmt"
+	"strings"
 
 	"git.frostfs.info/TrueCloudLab/frostfs-sdk-go/api/refs"
 	"github.com/mr-tron/base58"
@@ -123,3 +124,9 @@ func (x *ID) setUserID(w []byte) error {
 
 	return nil
 }
+
+// Cmp returns an integer comparing two base58 encoded user ID lexicographically.
+// The result will be 0 if id1 == id2, -1 if id1 < id2, and +1 if id1 > id2.
+func (x ID) Cmp(x2 ID) int {
+	return strings.Compare(x.EncodeToString(), x2.EncodeToString())
+}
diff --git a/user/id_test.go b/user/id_test.go
index c517dc5..c253336 100644
--- a/user/id_test.go
+++ b/user/id_test.go
@@ -3,6 +3,8 @@ package user_test
 import (
 	"bytes"
 	"crypto/rand"
+	"slices"
+	"strings"
 	"testing"
 
 	"git.frostfs.info/TrueCloudLab/frostfs-sdk-go/api/refs"
@@ -132,3 +134,16 @@ func TestID_Equal(t *testing.T) {
 	require.True(t, id3.Equals(id1)) // commutativity
 	require.False(t, id1.Equals(id2))
 }
+
+func TestID_Cmp(t *testing.T) {
+	id1 := usertest.ID()
+	id2 := usertest.ID()
+	id3 := usertest.ID()
+
+	arr := []ID{id1, id2, id3}
+
+	slices.SortFunc(arr, ID.Cmp)
+	for i := 1; i < len(arr); i++ {
+		require.NotEqual(t, strings.Compare(arr[i-1].EncodeToString(), arr[i].EncodeToString()), 1, "array is not sorted correctly")
+	}
+}