diff --git a/src/constant.js b/src/constant.js
index 52547342e..5dcef7da2 100644
--- a/src/constant.js
+++ b/src/constant.js
@@ -27,4 +27,4 @@ export const INVALID_DATE_STRING = 'Invalid Date'
 
 // regex
 export const REGEX_PARSE = /^(\d{4})[-/]?(\d{1,2})?[-/]?(\d{0,2})[Tt\s]*(\d{1,2})?:?(\d{1,2})?:?(\d{1,2})?[.:]?(\d+)?$/
-export const REGEX_FORMAT = /\[([^\]]+)]|YYYY|YY|M{1,4}|D{1,2}|d{1,4}|H{1,2}|h{1,2}|a|A|m{1,2}|s{1,2}|Z{1,2}|SSS/g
+export const REGEX_FORMAT = /\[([^\]]+)]|YYYY|YY|M{1,4}|D{1,2}|d{1,4}|H{1,2}|h{1,2}|a|A|m{1,2}|s{1,2}|Z{1,2}|S{1,3}/g
diff --git a/src/index.js b/src/index.js
index 061ade178..d06932daf 100644
--- a/src/index.js
+++ b/src/index.js
@@ -328,6 +328,10 @@ class Dayjs {
           return String(this.$s)
         case 'ss':
           return Utils.s(this.$s, 2, '0')
+        case 'S':
+          return String(Math.floor(this.$ms / 100))
+        case 'SS':
+          return Utils.s(Math.floor(this.$ms / 10), 2, '0')
         case 'SSS':
           return Utils.s(this.$ms, 3, '0')
         case 'Z':
diff --git a/test/plugin/customParseFormat_S_SS.test.js b/test/plugin/customParseFormat_S_SS.test.js
new file mode 100644
index 000000000..5d4cef10b
--- /dev/null
+++ b/test/plugin/customParseFormat_S_SS.test.js
@@ -0,0 +1,63 @@
+import dayjs from '../../src'
+import customParseFormat from '../../src/plugin/customParseFormat'
+
+dayjs.extend(customParseFormat)
+
+// Issue #1331: S and SS format tokens are not supported by the base format() function
+// This means:
+//   1. dayjs().format('S')  returns literal 'S'  instead of first digit of milliseconds
+//   2. dayjs().format('SS') returns literal 'SS' instead of first two digits of milliseconds
+//   3. customParseFormat strict mode fails with S/SS tokens
+
+describe('S and SS format tokens', () => {
+  describe('base format() support', () => {
+    it('format S returns first digit of milliseconds (hundreds)', () => {
+      expect(dayjs('2021-01-01T00:00:00.500').format('S')).toBe('5')
+      expect(dayjs('2021-01-01T00:00:00.900').format('S')).toBe('9')
+      expect(dayjs('2021-01-01T00:00:00.000').format('S')).toBe('0')
+    })
+
+    it('format SS returns first two digits of milliseconds', () => {
+      expect(dayjs('2021-01-01T00:00:00.520').format('SS')).toBe('52')
+      expect(dayjs('2021-01-01T00:00:00.050').format('SS')).toBe('05')
+      expect(dayjs('2021-01-01T00:00:00.000').format('SS')).toBe('00')
+    })
+
+    it('format SSS still works (3 digits)', () => {
+      expect(dayjs('2021-01-01T00:00:00.520').format('SSS')).toBe('520')
+      expect(dayjs('2021-01-01T00:00:00.005').format('SSS')).toBe('005')
+    })
+  })
+
+  describe('customParseFormat strict mode with S/SS tokens', () => {
+    it('SS strict mode parses 2-digit fractional seconds correctly', () => {
+      const result = dayjs(
+        '2021-01-01T00:00:00.52',
+        'YYYY-MM-DDTHH:mm:ss.SS',
+        true
+      )
+      expect(result.isValid()).toBe(true)
+      expect(result.millisecond()).toBe(520)
+    })
+
+    it('S strict mode parses 1-digit fractional seconds correctly', () => {
+      const result = dayjs(
+        '2021-01-01T00:00:00.5',
+        'YYYY-MM-DDTHH:mm:ss.S',
+        true
+      )
+      expect(result.isValid()).toBe(true)
+      expect(result.millisecond()).toBe(500)
+    })
+
+    it('SSS strict mode still works', () => {
+      const result = dayjs(
+        '2021-01-01T00:00:00.520',
+        'YYYY-MM-DDTHH:mm:ss.SSS',
+        true
+      )
+      expect(result.isValid()).toBe(true)
+      expect(result.millisecond()).toBe(520)
+    })
+  })
+})