The paper describes the procedure of theoretical investigations of dynamic processes in transmissions of transport and traction machines, in particular, torsional vibrations in a gear box of the K-744 tractor using modern software products. We used the MATHWORKS SIMSCAPE environment to develop algorithms tailored for engineering applications, providing a considerable reduction in computing. As an example, we have calculated an automated transmission aggregated with the ЯМЗ-5362 engine whose torque has a disturbing external influence and in certain conditions contributes to the emergence of resonance oscillations in the transmission. We have analyzed the simulation results of the engine–transmission system in the SIMSCAPE environment under testing load conditions. We have confirmed that the proposed algorithms are effective in comparison with alternative versions of the calculations.