Forging hammers are machines whose operation causes negative effects both at the place of their foundation (the soil settlement) and in their surroundings (e.g., vibrations propagating to the other devices, noise, etc.). Knowledge of the parameters characterizing the time history of the force that arises as a result of impact of a ram on a shaped material is of fundamental importance for the correct analysis of both the structure of the hammer and its impact on the surroundings. In the paper, the effect of the shape and duration of a pulse load on the dynamic response of a hammer-foundation forging system was assessed. An analytical method of description of the forces that arise as a result of impact of the ram on the forged material, using different forms of pulses was presented. The forces defined in this way as loads in a mathematical model of three degrees of freedom forging system were used. The equations of motion derived from d'Alembert's principle were solved numerically in the Matlab program. The analyses for eight forms of the pulse loads with the same pulse sizes but different durations were performed. The results in the graphs were presented. It was found, among other things, that a greater impact on the maximum displacement, velocity and acceleration of each component of the hammer-foundation system as well as on the maximum forces transmitted to the soil has the duration of a pulse than its shape.