diff --git a/packages/engine/Source/Core/EllipsoidRhumbLine.js b/packages/engine/Source/Core/EllipsoidRhumbLine.js
index 047d48e87961..51b410622677 100644
--- a/packages/engine/Source/Core/EllipsoidRhumbLine.js
+++ b/packages/engine/Source/Core/EllipsoidRhumbLine.js
@@ -333,10 +333,16 @@ function interpolateUsingSurfaceDistance(
     latitude = calculateInverseM(M2, ellipticity, major);
 
     //Now find the longitude of the second point
-    const sigma1 = calculateSigma(ellipticity, start.latitude);
-    const sigma2 = calculateSigma(ellipticity, latitude);
-    deltaLongitude = Math.tan(heading) * (sigma2 - sigma1);
-    longitude = CesiumMath.negativePiToPi(start.longitude + deltaLongitude);
+
+    // Check to see if the rhumb line has constant longitude
+    if (Math.abs(heading) < CesiumMath.EPSILON10) {
+      longitude = CesiumMath.negativePiToPi(start.longitude);
+    } else {
+      const sigma1 = calculateSigma(ellipticity, start.latitude);
+      const sigma2 = calculateSigma(ellipticity, latitude);
+      deltaLongitude = Math.tan(heading) * (sigma2 - sigma1);
+      longitude = CesiumMath.negativePiToPi(start.longitude + deltaLongitude);
+    }
   } else {
     //If heading is close to 90 degrees
     latitude = start.latitude;
diff --git a/packages/engine/Specs/Core/EllipsoidRhumbLineSpec.js b/packages/engine/Specs/Core/EllipsoidRhumbLineSpec.js
index f56803e3f411..87157adea73d 100644
--- a/packages/engine/Specs/Core/EllipsoidRhumbLineSpec.js
+++ b/packages/engine/Specs/Core/EllipsoidRhumbLineSpec.js
@@ -13,6 +13,7 @@ describe("Core/EllipsoidRhumbLine", function () {
   const fifteenDegrees = Math.PI / 12;
   const thirtyDegrees = Math.PI / 6;
   const fortyfiveDegrees = Math.PI / 4;
+  const threeHundredDegrees = (5 * Math.PI) / 6;
 
   it("throws without start", function () {
     expect(function () {
@@ -749,6 +750,46 @@ describe("Core/EllipsoidRhumbLine", function () {
     );
   });
 
+  it("interpolates when heading is near 90 degrees", function () {
+    const start = new Cartographic(0.0, 0.0);
+    const end = new Cartographic(Math.PI / 2, 0.0);
+    const expectedMid = new Cartographic(fortyfiveDegrees, 0.0);
+
+    const rhumb = new EllipsoidRhumbLine(start, end);
+    expect(rhumb.heading).toEqualEpsilon(Math.PI / 2, CesiumMath.EPSILON12);
+
+    const midpoint = rhumb.interpolateUsingFraction(0.5);
+
+    expect(expectedMid.longitude).toEqualEpsilon(
+      midpoint.longitude,
+      CesiumMath.EPSILON12
+    );
+    expect(expectedMid.latitude).toEqualEpsilon(
+      midpoint.latitude,
+      CesiumMath.EPSILON12
+    );
+  });
+
+  it("interpolates when heading is near 0 degrees", function () {
+    const start = new Cartographic(-threeHundredDegrees, fifteenDegrees);
+    const end = new Cartographic(-threeHundredDegrees, fortyfiveDegrees);
+    const expectedMid = new Cartographic(-threeHundredDegrees, thirtyDegrees);
+
+    const rhumb = new EllipsoidRhumbLine(start, end);
+    expect(rhumb.heading).toEqualEpsilon(0, CesiumMath.EPSILON12);
+
+    const midpoint = rhumb.interpolateUsingFraction(0.5);
+
+    expect(expectedMid.longitude).toEqualEpsilon(
+      midpoint.longitude,
+      CesiumMath.EPSILON12
+    );
+    expect(expectedMid.latitude).toEqualEpsilon(
+      midpoint.latitude,
+      CesiumMath.EPSILON3
+    );
+  });
+
   it("interpolates midpoint fraction using result parameter", function () {
     const start = new Cartographic(fifteenDegrees, 0.0);
     const end = new Cartographic(fortyfiveDegrees, 0.0);