Layered rough elliptical contact analysis is relevant in the rolling element industry, but existing models often oversimplify multi-axial curvatures, roughness, and layered materials. This work presents a 3D finite element implementation for simulating frictionless rough contacts in coated bodies, generating pseudo-elliptical contact areas. The contact is simplified to a flat deformable body with equivalent material properties against a rigid rough surface of equivalent curvatures, lowering computational cost. An efficient contact resolution algorithm that resolves overlaps and avoids artificial adhesion is introduced. Results match analytical and BEM solutions, with an order of magnitude speedup over the penalty method. Elliptical contact analysis shows that roughness asperities increase surface contact stresses and that coatings can contain high stresses inside the stronger layer.