The capability of PAM‐SHOCK, for studying the transient dynamic responses of a rolling tire impacting a road imperfection (“bump”) is presented. An industrial test case, that is, a tire rolling on a spinning drum that contains a cleat, was simulated using PAM‐SHOCK. The simulation includes pressurization of the tire, loading the tire against the drum and progressive rotating of the drum until the tire model reached a steady state rotation speed corresponding to 30 mph spindle velocity, and, finally, impacting of the tire with the cleat. The excess vertical and horizontal spindle force histories extracted from this simulation were studied and compared against experimental measurements. The similarities between them were identified. The simulation was further extended for six more repeated impacts corresponding to 21 tire revolutions to demonstrate the reliability of the program in providing a stable solution to the tire impact problem. The results are contrasted against the equivalent unstable calculation results.