The impact of a tool against a sonic transmission line is a subprocess of the impact coupling method of sonic power transfer. This process is modeled and the nonlinear governing equation developed in this paper. A probability density function is derived that enables the average rebound velocity of the impacting tool to be established. Numerical results are obtained, for selected material‐geometry parameters, on the stress pulses resulting from several conditions of impact, for the rebound velocity as a function of phase angle of impact and for the average rebound velocity. Future work will consider the entire impact coupling process and tools of more complex shape.