This paper presents the analysis of elastically supported beams using the element free Galerkin method (EFGM). The elastic support can be provided in the form of a load-bearing medium such as soil, distributed continuously along the length of the beam. This type of supports can be found in a variety of engineering problems, for example in the case of actual foundations or in the case of railroad track. The main difficulty in the analysis of the soil foundation interaction lies in the determination of the contact pressure. Any constitutive models may be used for simulating the action of the soil media. The finite element method has been used to model the beams on elastic foundations by representing continuity of the soil medium. However, the computations involved are more and has limited practical applications. In this paper, an attempt has been made to provide a simple but sufficiently accurate model for beams on elastic foundations using the meshfree technique, called as element free Galerkin method which does not rely on mesh. The formulation for the beams on elastic foundation is given for the governing equation which treats the soil in the form of rows of closely spaced independent elastic springs. The EFGM presented in the paper employs generalized moving least square approximants to approximate the function and transformation method for imposing the essential boundary conditions. Numerical examples are provided to study the convergence with various loading and boundary conditions. The results of the proposed method are compared with analytical solutions.