diff --git a/libs/geo/src/main/java/org/elasticsearch/geometry/Point.java b/libs/geo/src/main/java/org/elasticsearch/geometry/Point.java
index dc6a29db87bc0..bb390ad2d5cd1 100644
--- a/libs/geo/src/main/java/org/elasticsearch/geometry/Point.java
+++ b/libs/geo/src/main/java/org/elasticsearch/geometry/Point.java
@@ -16,6 +16,8 @@
  */
 public class Point implements Geometry {
     public static final Point EMPTY = new Point();
+    public static final String Z = "Z";
+    public static final String M = "M";
 
     private final double y;
     private final double x;
diff --git a/libs/geo/src/main/java/org/elasticsearch/geometry/utils/WellKnownText.java b/libs/geo/src/main/java/org/elasticsearch/geometry/utils/WellKnownText.java
index 9e657013a80dd..345e511454ad2 100644
--- a/libs/geo/src/main/java/org/elasticsearch/geometry/utils/WellKnownText.java
+++ b/libs/geo/src/main/java/org/elasticsearch/geometry/utils/WellKnownText.java
@@ -250,7 +250,6 @@ private static void parseGeometry(ByteBuffer byteBuffer, StringBuilder sb) {
             case 1018 -> parseBBox(byteBuffer, true, sb);
             default -> throw new IllegalArgumentException("Unknown geometry type: " + type);
         }
-        ;
     }
 
     private static void writeCoordinate(ByteBuffer byteBuffer, boolean hasZ, StringBuilder sb) {
@@ -472,15 +471,23 @@ private static GeometryCollection<Geometry> parseGeometryCollection(StreamTokeni
     }
 
     private static Point parsePoint(StreamTokenizer stream) throws IOException, ParseException {
-        if (nextEmptyOrOpen(stream).equals(EMPTY)) {
+        if (isEmptyNext(stream)) {
             return Point.EMPTY;
         }
+        String token = nextZOrMOrOpen(stream);
+        boolean hasZOrM = token.equals(Point.Z) || token.equals(Point.M);
+        if (hasZOrM) {
+            nextOpener(stream);
+        }
         double lon = nextNumber(stream);
         double lat = nextNumber(stream);
         Point pt;
         if (isNumberNext(stream)) {
             pt = new Point(lon, lat, nextNumber(stream));
         } else {
+            if (hasZOrM) {
+                throw new ParseException("'POINT Z' or 'POINT M' must have three coordinates, but only two were found.", stream.lineno());
+            }
             pt = new Point(lon, lat);
         }
         nextCloser(stream);
@@ -710,6 +717,14 @@ private static boolean isNumberNext(StreamTokenizer stream) throws IOException {
         return type == StreamTokenizer.TT_WORD;
     }
 
+    private static boolean isEmptyNext(StreamTokenizer stream) throws ParseException, IOException {
+        if (nextWord(stream).equals(EMPTY)) {
+            return true;
+        }
+        stream.pushBack();
+        return false;
+    }
+
     private static String nextEmptyOrOpen(StreamTokenizer stream) throws IOException, ParseException {
         final String next = nextWord(stream);
         if (next.equals(EMPTY) || next.equals(LPAREN)) {
@@ -718,6 +733,17 @@ private static String nextEmptyOrOpen(StreamTokenizer stream) throws IOException
         throw new ParseException("expected " + EMPTY + " or " + LPAREN + " but found: " + tokenString(stream), stream.lineno());
     }
 
+    private static String nextZOrMOrOpen(StreamTokenizer stream) throws ParseException, IOException {
+        final String next = nextWord(stream);
+        if (next.equals(Point.Z) || next.equals(Point.M) || next.equals(LPAREN)) {
+            return next;
+        }
+        throw new ParseException(
+            "expected " + LPAREN + " or " + Point.Z + " or " + Point.M + " but found: " + tokenString(stream),
+            stream.lineno()
+        );
+    }
+
     private static String nextCloser(StreamTokenizer stream) throws IOException, ParseException {
         if (nextWord(stream).equals(RPAREN)) {
             return RPAREN;
diff --git a/libs/geo/src/test/java/org/elasticsearch/geometry/PointTests.java b/libs/geo/src/test/java/org/elasticsearch/geometry/PointTests.java
index b61c36579bfca..56db8c2050217 100644
--- a/libs/geo/src/test/java/org/elasticsearch/geometry/PointTests.java
+++ b/libs/geo/src/test/java/org/elasticsearch/geometry/PointTests.java
@@ -17,6 +17,7 @@
 
 import java.io.IOException;
 import java.text.ParseException;
+import java.util.List;
 
 public class PointTests extends BaseGeometryTestCase<Point> {
     @Override
@@ -58,6 +59,52 @@ public void testWKTValidation() {
         assertEquals("found Z value [100.0] but [ignore_z_value] parameter is [false]", ex.getMessage());
     }
 
+    public void testParsePointZWithThreeCoordinates() throws IOException, ParseException {
+        GeometryValidator validator = GeographyValidator.instance(true);
+        assertEquals(new Point(20, 10, 100), WellKnownText.fromWKT(validator, true, "POINT Z (20.0 10.0 100.0)"));
+    }
+
+    public void testParsePointMWithThreeCoordinates() throws IOException, ParseException {
+        GeometryValidator validator = GeographyValidator.instance(true);
+        assertEquals(new Point(20, 10, 100), WellKnownText.fromWKT(validator, true, "POINT M (20.0 10.0 100.0)"));
+    }
+
+    public void testParsePointZWithTwoCoordinatesThrowsException() {
+        GeometryValidator validator = GeographyValidator.instance(true);
+        ParseException ex = expectThrows(ParseException.class, () -> WellKnownText.fromWKT(validator, true, "POINT Z (20.0 10.0)"));
+        assertEquals("'POINT Z' or 'POINT M' must have three coordinates, but only two were found.", ex.getMessage());
+    }
+
+    public void testParsePointMWithTwoCoordinatesThrowsException() {
+        GeometryValidator validator = StandardValidator.instance(true);
+        ParseException ex = expectThrows(ParseException.class, () -> WellKnownText.fromWKT(validator, true, "POINT M (20.0 10.0)"));
+        assertEquals("'POINT Z' or 'POINT M' must have three coordinates, but only two were found.", ex.getMessage());
+    }
+
+    public void testParsePointZMFormatNotSupported() {
+        GeometryValidator validator = StandardValidator.instance(true);
+        List<String> points = List.of("POINT ZM (20.0 10.0 100.0 200.0)", "POINT ZM (20.0 10.0 100.0)", "POINT ZM (20.0 10.0)");
+        for (String point : points) {
+            ParseException ex = expectThrows(ParseException.class, () -> WellKnownText.fromWKT(validator, true, point));
+            assertEquals("expected ( or Z or M but found: ZM", ex.getMessage());
+        }
+    }
+
+    public void testParsePointZWithEmpty() {
+        GeometryValidator validator = StandardValidator.instance(true);
+        ParseException ex = expectThrows(ParseException.class, () -> WellKnownText.fromWKT(validator, true, "POINT Z EMPTY"));
+        assertEquals("expected ( but found: EMPTY", ex.getMessage());
+    }
+
+    public void testParsePointZOrMWithTwoCoordinates() {
+        GeometryValidator validator = StandardValidator.instance(true);
+        List<String> points = List.of("POINT Z (20.0 10.0)", "POINT M (20.0 10.0)");
+        for (String point : points) {
+            ParseException ex = expectThrows(ParseException.class, () -> WellKnownText.fromWKT(validator, true, point));
+            assertEquals("'POINT Z' or 'POINT M' must have three coordinates, but only two were found.", ex.getMessage());
+        }
+    }
+
     @Override
     protected Point mutateInstance(Point instance) {
         return null;// TODO implement https://github.com/elastic/elasticsearch/issues/25929