diff --git a/CHANGES.md b/CHANGES.md
index 127a05c942b5..a660b73f7f9f 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -23,6 +23,8 @@ Change Log
 * 3D Tiles geometric error now scales with transform. [#8182](https://github.com/AnalyticalGraphicsInc/cesium/pull/8182)
 * Fixed per-feature post processing from sometimes selecting the wrong feature. [#7929](https://github.com/AnalyticalGraphicsInc/cesium/pull/7929)
 * Fixed labels not showing for individual entities in data sources when clustering is enabled. [#6087](https://github.com/AnalyticalGraphicsInc/cesium/issues/6087)
+* Fixed a crash for 3D Tiles that have zero volume. [#7945](https://github.com/AnalyticalGraphicsInc/cesium/pull/7945)
+
 
 ### 1.61 - 2019-09-03
 
diff --git a/Source/Scene/TileBoundingSphere.js b/Source/Scene/TileBoundingSphere.js
index 278e11ad8a51..724fb4f07df7 100644
--- a/Source/Scene/TileBoundingSphere.js
+++ b/Source/Scene/TileBoundingSphere.js
@@ -7,6 +7,7 @@ define([
         '../Core/GeometryInstance',
         '../Core/Matrix4',
         '../Core/SphereOutlineGeometry',
+        '../Core/Math',
         './PerInstanceColorAppearance',
         './Primitive'
     ], function(
@@ -18,6 +19,7 @@ define([
         GeometryInstance,
         Matrix4,
         SphereOutlineGeometry,
+        CesiumMath,
         PerInstanceColorAppearance,
         Primitive) {
     'use strict';
@@ -33,6 +35,9 @@ define([
      * @private
      */
     function TileBoundingSphere(center, radius) {
+        if (radius === 0) {
+            radius = CesiumMath.EPSILON7;
+        }
         this._boundingSphere = new BoundingSphere(center, radius);
     }
 
diff --git a/Source/Scene/TileOrientedBoundingBox.js b/Source/Scene/TileOrientedBoundingBox.js
index c1f0ef277694..1bcafc5a9732 100644
--- a/Source/Scene/TileOrientedBoundingBox.js
+++ b/Source/Scene/TileOrientedBoundingBox.js
@@ -9,6 +9,7 @@ define([
         '../Core/Matrix3',
         '../Core/Matrix4',
         '../Core/OrientedBoundingBox',
+        '../Core/Math',
         './PerInstanceColorAppearance',
         './Primitive'
     ], function(
@@ -22,10 +23,70 @@ define([
         Matrix3,
         Matrix4,
         OrientedBoundingBox,
+        CesiumMath,
         PerInstanceColorAppearance,
         Primitive) {
     'use strict';
 
+    var scratchU = new Cartesian3();
+    var scratchV = new Cartesian3();
+    var scratchW = new Cartesian3();
+    var scratchCartesian = new Cartesian3();
+
+    function computeMissingVector(a, b, result) {
+        result = Cartesian3.cross(a, b, result);
+        var magnitude = Cartesian3.magnitude(result);
+        return Cartesian3.multiplyByScalar(result, CesiumMath.EPSILON7 / magnitude, result);
+    }
+
+    function findOrthogonalVector(a, result) {
+        var temp = Cartesian3.normalize(a, scratchCartesian);
+        var b = Cartesian3.equalsEpsilon(temp, Cartesian3.UNIT_X, CesiumMath.EPSILON6) ? Cartesian3.UNIT_Y : Cartesian3.UNIT_X;
+        return computeMissingVector(a, b, result);
+    }
+
+    function checkHalfAxes(halfAxes) {
+        var u = Matrix3.getColumn(halfAxes, 0, scratchU);
+        var v = Matrix3.getColumn(halfAxes, 1, scratchV);
+        var w = Matrix3.getColumn(halfAxes, 2, scratchW);
+
+        var uZero = Cartesian3.equals(u, Cartesian3.ZERO);
+        var vZero = Cartesian3.equals(v, Cartesian3.ZERO);
+        var wZero = Cartesian3.equals(w, Cartesian3.ZERO);
+
+        if (!uZero && !vZero && !wZero) {
+            return halfAxes;
+        }
+        if (uZero && vZero && wZero) {
+            halfAxes[0] = CesiumMath.EPSILON7;
+            halfAxes[4] = CesiumMath.EPSILON7;
+            halfAxes[8] = CesiumMath.EPSILON7;
+            return halfAxes;
+        }
+        if (uZero && !vZero && !wZero) {
+            u = computeMissingVector(v, w, u);
+        } else if (!uZero && vZero && !wZero) {
+            v = computeMissingVector(u, w, v);
+        } else if (!uZero && !vZero && wZero) {
+            w = computeMissingVector(v, u, w);
+        } else if (!uZero) {
+            v = findOrthogonalVector(u, v);
+            w = computeMissingVector(v, u, w);
+        } else if (!vZero) {
+            u = findOrthogonalVector(v, u);
+            w = computeMissingVector(v, u, w);
+        } else if (!wZero) {
+            u = findOrthogonalVector(w, u);
+            v = computeMissingVector(w, u, v);
+        }
+
+        Matrix3.setColumn(halfAxes, 0, u, halfAxes);
+        Matrix3.setColumn(halfAxes, 1, v, halfAxes);
+        Matrix3.setColumn(halfAxes, 2, w, halfAxes);
+
+        return halfAxes;
+    }
+
     /**
      * A tile bounding volume specified as an oriented bounding box.
      * @alias TileOrientedBoundingBox
@@ -39,6 +100,7 @@ define([
      * @private
      */
     function TileOrientedBoundingBox(center, halfAxes) {
+        halfAxes = checkHalfAxes(halfAxes);
         this._orientedBoundingBox = new OrientedBoundingBox(center, halfAxes);
         this._boundingSphere = BoundingSphere.fromOrientedBoundingBox(this._orientedBoundingBox);
     }
@@ -111,6 +173,7 @@ define([
      */
     TileOrientedBoundingBox.prototype.update = function(center, halfAxes) {
         Cartesian3.clone(center, this._orientedBoundingBox.center);
+        halfAxes = checkHalfAxes(halfAxes);
         Matrix3.clone(halfAxes, this._orientedBoundingBox.halfAxes);
         BoundingSphere.fromOrientedBoundingBox(this._orientedBoundingBox, this._boundingSphere);
     };
@@ -128,8 +191,8 @@ define([
 
         var geometry = new BoxOutlineGeometry({
             // Make a 2x2x2 cube
-            minimum: new Cartesian3(-1.0, -1.0, -1.0),
-            maximum: new Cartesian3(1.0, 1.0, 1.0)
+            minimum : new Cartesian3(-1.0, -1.0, -1.0),
+            maximum : new Cartesian3(1.0, 1.0, 1.0)
         });
         var modelMatrix = Matrix4.fromRotationTranslation(this.boundingVolume.halfAxes, this.boundingVolume.center);
         var instance = new GeometryInstance({
diff --git a/Specs/Scene/Cesium3DTileSpec.js b/Specs/Scene/Cesium3DTileSpec.js
index 3dfb834ccce8..0095f58ac7be 100644
--- a/Specs/Scene/Cesium3DTileSpec.js
+++ b/Specs/Scene/Cesium3DTileSpec.js
@@ -240,6 +240,33 @@ describe('Scene/Cesium3DTile', function() {
             expect(tile.boundingVolume).toEqual(obb);
         });
 
+        it('does not crash for bounding box with 0 volume', function() {
+            // Create a copy of the tile with bounding box.
+            var tileWithBoundingBox0Volume = JSON.parse(JSON.stringify(tileWithBoundingBox));
+            // Generate all the combinations of missing axes.
+            var boxes = [];
+            for (var x = 0; x < 2; ++x) {
+                for (var y = 0; y < 2; ++y) {
+                    for (var z = 0; z < 2; ++z) {
+                        boxes.push([0.0, 0.0, 0.0, x, 0.0, 0.0, 0.0, y, 0.0, 0.0, 0.0, z]);
+                    }
+                }
+            }
+
+            for (var i = 0; i < boxes.length; ++i) {
+                var box = boxes[i];
+
+                tileWithBoundingBox0Volume.boundingVolume.box = box;
+
+                var tile = new Cesium3DTile(mockTileset, '/some_url', tileWithBoundingBox0Volume, undefined);
+                expect(tile.boundingVolume).toBeDefined();
+                var center = new Cartesian3(box[0], box[1], box[2]);
+                var halfAxes = Matrix3.fromArray(box, 3);
+                var obb = new TileOrientedBoundingBox(center, halfAxes);
+                expect(tile.boundingVolume).toEqual(obb);
+            }
+        });
+
         it('can have a content oriented bounding box', function() {
             var box = tileWithContentBoundingBox.boundingVolume.box;
             var tile = new Cesium3DTile(mockTileset, '/some_url', tileWithContentBoundingBox, undefined);