Over the past decades, pile foundations used to support buildings through a transfer of superstructure loads into more stable soil strata than surface soil layers. Buildings are exposed to seismic force, pile undergoes more stress through the significant vibration of the surrounding soil in addition to the static stresses of buildings. The investigation of the behavior of pile foundations under the influence of earthquakes is still limited or not well described. Further, this paper presents a theoretical study to evaluate the vertical settlement and horizontal displacement of piles embedded in clay and silty soil of Baqubah soil under the effect of the acceleration time history of the 1940 El-Centro earthquake. The study was carried out by using the commercial finite element software PLAXIS 3D. A three-dimensional analysis of the soil-pile foundation for four multi-story buildings is performed with different diameters (0.5, 0.7, and 1) m for the corner, exterior, and interior pile, respectively. The linear elastic model for pile foundation and the Mohr-Coulomb model for soil layers were used in this numerical analysis. The research showed that vertical settlement and horizontal displacement increase as the duration of the earthquake increases, and horizontal displacement with values smaller than vertical displacement. Also, the results showed the vertical settlement is similar for different diameters, in contrast to the horizontal displacement, which was of different values with a range between (3% to 22%) when the diameter increased from 0.5m, 0.7m, and 1m. Also, it can be observed that values increased with the direction of the earthquake from the right to the left side of the pile-soil system with a range of (12% to 32%).