Abstract: An equality checking approach for 3D solid models is presented. In this approach, first, invariants like types and numbers of geometric and topological elements in the models are compared to exclude dissimilar parts. Second, the residual parts are transformed to the same position and orientation coincident to their inertia coordinate systems. Then, the equalities of the models' elements are checked. This method is proved to be valid and efficient for counting mechanical parts with boundaries composed of planes and quadratic surfaces.