Improving in assembling technology has provided machines of higher evaluation with better resistances and managed behavior. This machinery led to remarkably higher dynamic forces and therefore higher stresses. In this paper, a dynamic investigation of rectangular machine diesel and gas engines foundation at the top surface of one-layer dry sand with various states (i.e., loose, medium and dense) was carried out. The dynamic investigation is performed numerically by utilizing limited component programming, PLAXIS 3D. The soil is accepted as flexible totally plastic material submits to Mohr-Coulomb yield basis. A harmonic load is applied at the foundation with amplitude of 10 kPa at a frequency of (10, 15 and 20) HZ and seismic load is applied with acceleration – time input of earthquake hit Halabjah city north of Iraq. A parametric statement is completed to evaluate the effect of changing the relative density, embedded depth and frequency of the machine. It has been noticed that the relative density plays an important role in the resistance of settlement, as it increases the resistance of the soil to the applied loads because the dense soil is stiffer. While total stress and displacement of different relative density decrease at the time when increasing the foundations' embedding, the ratio was (15%) at the depths (Df=0 and Df=2). In addition, it has been noticed that there decrease of displacement when the frequency value changes from (10 to 20) Hz.