A new solution method for the oblique elastic impact of similar spheres with Coulomb friction is presented. The solution uses approximations of the shear stress distributions at each time step during impact. These distributions are solved from analytical formulations and are able to account for both full sliding and partial-slip scenarios that may both be present for this problem due to inclusion of tangential compliance and friction effects. Comparison to previous continuum models in the literature shows very good agreement for the contact force wave forms obtained. The major advantage of this method is the drastic reduction in computation time required compared to previous solutions.