In this paper, we have given numerical solution of the elasticity problem of settled on the wronkler ground with variable coefficient. The approximation solution of boundary value problem which is pertinent to this has been converted to integral equations, and then by using the successive approximation methods, has been reached. In addition to this, the approximation solution of the problem was put into Padé series form. We applied these methods to an example which is the elasticity problem of unit length homogeny beam, which is a special form of boundary value problem. First we calculate the successive approximation of the given boundary value problem then transform it into Padé series form, which give an arbitrary order for solving differential equation numerically.