diff --git a/core/src/main/scala/org/apache/spark/ui/UIUtils.scala b/core/src/main/scala/org/apache/spark/ui/UIUtils.scala
index 4cbc45e033503..74bb78a227657 100644
--- a/core/src/main/scala/org/apache/spark/ui/UIUtils.scala
+++ b/core/src/main/scala/org/apache/spark/ui/UIUtils.scala
@@ -21,7 +21,8 @@ import java.{util => ju}
 import java.lang.{Long => JLong}
 import java.net.URLDecoder
 import java.nio.charset.StandardCharsets.UTF_8
-import java.text.SimpleDateFormat
+import java.time.{Instant, ZoneId}
+import java.time.format.DateTimeFormatter
 import java.util.{Date, Locale, TimeZone}
 import javax.servlet.http.HttpServletRequest
 import javax.ws.rs.core.{MediaType, MultivaluedMap, Response}
@@ -42,15 +43,14 @@ private[spark] object UIUtils extends Logging {
   val TABLE_CLASS_STRIPED = TABLE_CLASS_NOT_STRIPED + " table-striped"
   val TABLE_CLASS_STRIPED_SORTABLE = TABLE_CLASS_STRIPED + " sortable"
 
-  // SimpleDateFormat is not thread-safe. Don't expose it to avoid improper use.
-  private val dateFormat = new ThreadLocal[SimpleDateFormat]() {
-    override def initialValue(): SimpleDateFormat =
-      new SimpleDateFormat("yyyy/MM/dd HH:mm:ss", Locale.US)
-  }
+  private val dateTimeFormatter = DateTimeFormatter
+    .ofPattern("yyyy/MM/dd HH:mm:ss", Locale.US)
+    .withZone(ZoneId.systemDefault())
 
-  def formatDate(date: Date): String = dateFormat.get.format(date)
+  def formatDate(date: Date): String = dateTimeFormatter.format(date.toInstant)
 
-  def formatDate(timestamp: Long): String = dateFormat.get.format(new Date(timestamp))
+  def formatDate(timestamp: Long): String =
+    dateTimeFormatter.format(Instant.ofEpochMilli(timestamp))
 
   def formatDuration(milliseconds: Long): String = {
     if (milliseconds < 100) {
@@ -124,16 +124,13 @@ private[spark] object UIUtils extends Logging {
     }
   }
 
-  // SimpleDateFormat is not thread-safe. Don't expose it to avoid improper use.
-  private val batchTimeFormat = new ThreadLocal[SimpleDateFormat]() {
-    override def initialValue(): SimpleDateFormat =
-      new SimpleDateFormat("yyyy/MM/dd HH:mm:ss", Locale.US)
-  }
+  private val batchTimeFormat = DateTimeFormatter
+    .ofPattern("yyyy/MM/dd HH:mm:ss", Locale.US)
+    .withZone(ZoneId.systemDefault())
 
-  private val batchTimeFormatWithMilliseconds = new ThreadLocal[SimpleDateFormat]() {
-    override def initialValue(): SimpleDateFormat =
-      new SimpleDateFormat("yyyy/MM/dd HH:mm:ss.SSS", Locale.US)
-  }
+  private val batchTimeFormatWithMilliseconds = DateTimeFormatter
+    .ofPattern("yyyy/MM/dd HH:mm:ss.SSS", Locale.US)
+    .withZone(ZoneId.systemDefault())
 
   /**
    * If `batchInterval` is less than 1 second, format `batchTime` with milliseconds. Otherwise,
@@ -150,19 +147,19 @@ private[spark] object UIUtils extends Logging {
       batchInterval: Long,
       showYYYYMMSS: Boolean = true,
       timezone: TimeZone = null): String = {
-    val oldTimezones =
-      (batchTimeFormat.get.getTimeZone, batchTimeFormatWithMilliseconds.get.getTimeZone)
+    val oldTimezones = (batchTimeFormat.getZone, batchTimeFormatWithMilliseconds.getZone)
     if (timezone != null) {
-      batchTimeFormat.get.setTimeZone(timezone)
-      batchTimeFormatWithMilliseconds.get.setTimeZone(timezone)
+      val zoneId = timezone.toZoneId
+      batchTimeFormat.withZone(zoneId)
+      batchTimeFormatWithMilliseconds.withZone(zoneId)
     }
     try {
       val formattedBatchTime =
         if (batchInterval < 1000) {
-          batchTimeFormatWithMilliseconds.get.format(batchTime)
+          batchTimeFormatWithMilliseconds.format(Instant.ofEpochMilli(batchTime))
         } else {
           // If batchInterval >= 1 second, don't show milliseconds
-          batchTimeFormat.get.format(batchTime)
+          batchTimeFormat.format(Instant.ofEpochMilli(batchTime))
         }
       if (showYYYYMMSS) {
         formattedBatchTime
@@ -171,8 +168,8 @@ private[spark] object UIUtils extends Logging {
       }
     } finally {
       if (timezone != null) {
-        batchTimeFormat.get.setTimeZone(oldTimezones._1)
-        batchTimeFormatWithMilliseconds.get.setTimeZone(oldTimezones._2)
+        batchTimeFormat.withZone(oldTimezones._1)
+        batchTimeFormatWithMilliseconds.withZone(oldTimezones._2)
       }
     }
   }
diff --git a/sql/core/src/main/scala/org/apache/spark/sql/streaming/ui/UIUtils.scala b/sql/core/src/main/scala/org/apache/spark/sql/streaming/ui/UIUtils.scala
index 88a110fa9a329..c031ec39511f5 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/streaming/ui/UIUtils.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/streaming/ui/UIUtils.scala
@@ -17,9 +17,10 @@
 
 package org.apache.spark.sql.streaming.ui
 
-import java.text.SimpleDateFormat
+import java.time.ZonedDateTime
+import java.time.format.DateTimeFormatter
 
-import org.apache.spark.sql.catalyst.util.DateTimeUtils.getTimeZone
+import org.apache.spark.sql.catalyst.util.DateTimeUtils.getZoneId
 
 private[ui] object UIUtils {
 
@@ -62,15 +63,12 @@ private[ui] object UIUtils {
     }
   }
 
-  private val progressTimestampFormat = new ThreadLocal[SimpleDateFormat]() {
-    override def initialValue(): SimpleDateFormat = {
-      val format = new SimpleDateFormat("yyyy-MM-dd'T'HH:mm:ss.SSS'Z'") // ISO8601
-      format.setTimeZone(getTimeZone("UTC"))
-      format
-    }
-  }
+  private val progressTimestampFormat = DateTimeFormatter
+    .ofPattern("yyyy-MM-dd'T'HH:mm:ss.SSS'Z'") // ISO8601
+    .withZone(getZoneId("UTC"))
 
   def parseProgressTimestamp(timestamp: String): Long = {
-    progressTimestampFormat.get.parse(timestamp).getTime
+    val zonedDateTime = ZonedDateTime.parse(timestamp, progressTimestampFormat)
+    zonedDateTime.toInstant.toEpochMilli
   }
 }