I've attached the simplest implementation using a Lab modifier - a collider object dents the target object by pushing its vertices inside along their normals. It's a Max 2014 scene with a plane and a sphere, the sphere is animated to show the effect on the plane. The Skew modifier on the plane (which is disabled initially) improves a bit the topology of the mesh, giving a slightly smoother result around the edges. And applying a MeshSmooth over the LabPolygonModifier would further smooth out the result.
I have no idea though what formula could be used for the bulge, I'm open to suggestions. I'm also thinking of a way to further smooth the initial result by pushing along the vertices that are not directly affected by the sphere, but are close to the pushed ones.
I also attach the .ctx file containing the Lab modifier, in case you can't open the scene for some reason. Just create a sphere and a plane, add a LabPolygonModifier to the plane, open the editor, load the .ctx file, then select the sphere as collider in Command Panel. I'm assuming that you have the Lab demo version installed. If not, I could send you screen shots, renderings, or I could bake the plane using a PointCache.