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A two-dimensional (2D) finite element analysis was carried out to assess the time-dependent behavior of single vertical pile embedded in elasto-plastic soil. The finite element analyses were carried out using the linear elastic model for the structure of the pile, while the Mohr-Coulomb model was used for representing the soil behavior surrounding the pile. The study includes cohesionless and cohesive soil to assess the lateral response of pile in the two types of soil. The whole geotechnical model is suitable for problem of piles to determine the design quantities such as lateral deformation, lateral soil stress and its variation with time. The model is verified based on the results of published cases and there is good comparison between the results of published case and the present simulation model. It is found that, the pile in cohesionless soil has more resistance in the rapid loading and less one in the long term loading. On the other hand, the pile in cohesive soil shows opposite behavior.