In this paper a mathematical formulation and a numerical algorithm for the analysis of impact of rigid bodies against rigid obstacles are developed. The paper concentrates on three-dimensional motion using a direct approach where the impenetrability condition and Coulomb's law of friction are formulated as equations, which are not differentiable in the usual sense, and solved together with the equations of motion and necessary kinematical relations using Newton's method. An experiment has also been performed and compared with predictions of the algorithm, with favorable results.