A computational methodology for dynamic analysis of multibody mechanical systems with joint clearance is presented in this work. Clearances always exist in real joints in order to ensure the correct relative motion between the connected bodies being the gap associated to them a result of machining tolerance, wear, and local deformations. Clearance at different joints is the source for impact forces, resulting in wear and tear of the joints, and consequently the degradation of the system performance. The model for planar revolute joints is based on a thorough geometric description of contact conditions and on a continuous contact force model, which represents the impact forces. It is shown that the model proposed here lead to realistic contact forces. These forces correlate well with the joint reaction forces of an ideal revolute joint, which correspond to a null joint clearance. The application to the analysis of a simple planar multibody system illustrates the use of the different models proposed.