In this paper, a dynamic investigation is done for strip, rectangular and square machine foundation at the top surface of two-layer dry sand with various states (i.e., loose on medium sand and dense on medium sand). The dynamic investigation is performed numerically using finite element programming, PLAXIS 3D. The soil is expected as a versatile totally plastic material that complies with the Mohr-Coulomb yield criterion. A harmonic load is applied at the base with an amplitude of 6 kPa at a frequency of (2 and 6) Hz, and seismic is applied with acceleration – time input of earthquake hit Halabjah city north of Iraq. A parametric study is done to evaluate the influence of changing L/B ratio (Length=12,6,3 m and width=3 m), type of sand, and frequency of the machine for soil with two layers (dense and medium sand) and (loose and medium sand). It was noticed that the displacement decreases when the foundation is strip, and has the highest values when the foundation is square. At the same time, the maximum vertical stress of the foundation (L/B = 4 and L/B = 1) appears to be (1262) kPa and (1255) kPa, respectively, due to increasing the foundation mass as a result of increasing its dimensions. Then again, the displacement increases by 20% for vertical displacement when decreasing the relative density. In addition, it has been noticed that there is a decrease in displacement when the frequency value changes from (2 to 6) Hz.
