In this paper, we have given numerical solutions of the elasticity problem of settled on the elastic ground with variable coefficient. Firstly, we calculate the generalized successive approximation of the given boundary value problem and we transform it into Pade series form, which give an arbitrary order for solving differential equation numerically. Secondly, we apply Homotopy Perturbation Method(HPM) to given boundary value problem. Then we compare HPM and the generalized successive approximation -Pade Approximates method by means of numerical solution of given boundary problem. Results reveal that HPM presents more effective and accurate solution for given boundary value problem.