Abstract: In this study a discrete semi analytical method based on a combination of the Finite Elements, Thin Layers and Integral Equations Methods is presented to evaluate the vertical static and dynamic linear response of a pile foundation subjected to a vertical load. This study, which takes into account the soil-pile interaction effects, is able to treat the case of an arbitrary shaped pile. However, the presentation will be limited to the case of a massless square pile with linear elastic behaviour. The pile is embedded in a viscoelastic soil-layer overlaying a bedrock and subjected to static or/and harmonic vertical load, applied at the head of the pile. The aim of this study is to characterise the response of a pile through the force-displacement relationship. Numerical results are presented to illustrate the accuracy of this study.