Soil pile interaction problem, under dynamic loading condition, has drawn the attention since 1934. In this paper a time domain approach of the soil pile interaction problem, under lateral dynamic loading, has been attempted. The material property of the vertical pile is linearly elastic homogeneous and isotropic. The motion of the pile is limited in the vertical plane. The time domain has been discretised into small intervals. The non linearity of soil property has been taken into account by using equivalent linear (ELM) soil properties. The need for non linear analysis becomes particularly important when soil system experience a large non recoverable strain. The inadequacy of linear models in describing the hysteritic energy dissipation mechanism demands the necessity of incorporating a truly non linéar formulation of the problem. Suitable software has been developed which keeps track of the stress path and load reversal points of each element and the computer program takes decision about the appropriate instantaneous soil properties. In the experimental part of the work authors have carried out a small scale test, in the laboratory. Model pile embedded in dry dense sand in a tank was excited under two different dynamic loading conditions. In the first study the base of the tank was excited by a large motor and oscillator assembly and the pile top was free. In the second case the pile top was excited by a small motor and oscillator assembly and the base was at rest. The acceleration response of the pile was recorded with proper data acquisition system for both the cases. Comparison of the experimental and numerical studies have revealed that a proper judgement on the mathematical modelling of soil behaviour is very essential for any reliable analytical prediction.