A thin elastic rod is clamped between two rigid plates. The governing partial differential equation is nonlinear owing to the presence of Coulomb friction, which acts at the surfaces of contact. The displacement, velocity, and strain may be solved for when a stress pulse is applied for particular time periods. The stress wave penetrates the rod to a depth which depends on the applied stress and the friction force. When the motion of the rod is entirely damped out by the friction, a residual stress distribution remains.