The present studies emphasis the analysis of beam for elastic foundation using the Element Free Galerkine Method (EFGM). The attempt was made to provide a simple model for beams on elastic foundation using Mesh Free Technique, called as Element Free Galerkine Method which does not rely on the mesh. The EFGM presented in the study employs generalized Method of Least Square (MLS), which is used to construct shape function based on the set of nodes. The Discrete system equation are derived from the variation form of system equation. A FORTRAN and MATLAB program is developed and numerical example of finite and infinite beams on elastic foundation are presented. Numerical examples are provided to study the convergence and the efficiency of the method.