One of mesh free methods, element free Galerkin method, is presented to analyze the finite beam on elastic foundation. The shape functions are constructed by using the moving least square interpolation based on a set of nodes that are arbitrarily distributed in specified domain. Discrete system equations are derived from the variation form of system equations. Numerical examples of finite beam on elastic foundation are given by establishing Matlab code. The results of this paper demonstrate the

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... effectiveness of the proposed method with small errors compared to analytical solutions. Keywords: mesh free method, element free Galerkin method, moving least square, finite beam, elastic foundation.