In this research the accuracy of the numerical results obtained from two different numerical methods was checked by simulating the pile-supported machine foundation under coupled dynamic loads. In order to accomplish this, finite element and finite difference methods are chosen which are available as PLAXIS-3D and FLAC-3D, respectively. Hollow steel pile of length of 5.8 m and diameter of 0.166 m with thickness of 0.007 m is simulated. Linear elastic model is used for a pile and steel plates, Mohr–Coulomb failure criterion is employed for the soil layers. The dynamic analysis has been conducted at different magnitudes of dynamic loads (We 0.735, 1.448, 2.117, and 2.721 Nm). The obtained results from both analyses are compared with the available literature. Both numerical methods estimated two peaks within the 50 Hz frequency. However, the FEM method overestimated the first peaks of both horizontal and rocking amplitudes and their corresponding resonant frequencies. Conversely, second peaks and respective resonant frequencies are underestimated. FLAC-3D underestimated first and second peaks of the horizontal and rocking amplitudes and overestimated their resonant amplitudes. Both analyses simulated the nonlinear behavior of soil as there is shift in resonant amplitudes and corresponding frequencies with the dynamic loads. FEM results are more harmonious than FDM.