An original design and the operation principle of horizontal bidirectional bump testing machine with pendulum seismic mass are proposed. A schematic diagram and a mathematical model of the testing system have been developed. The adequacy of the model is confirmed by the experimental data obtained from tests on the SOUG2000-type bump machine developed by DeltaMec. Simulation results of the motion trajectories of the machine’s main components are presented. Parameters of the pneumatic suspension system were analyzed to reduce dynamic loads on the workshop equipment following shock reproduction. A setup procedure for the testing machine is proposed to achieve the desired parameters of the shock impulse. This procedure is based on setting the initial air pressure in the receiver and selecting an appropriate shock programmer.