Abstract: The method of double Fourier transform was introduced for the analysis of an elastic half space loaded with vertical force,and an integral representation for displacements of an elastic half space was presented.The analytic solution of an elastic rectangular plate on an elastic half space was also given by combining the analytic solution of an elastic rectangular plate with four free edges.Some examples were analyzed and the results were compared with those from the literature which used other methods such as finite element method.The agreement was found to be satisfactory which proved the validity of the new method in solving the problem of a rectangular plate on an elastic half space with four free edges.This new method would be feasible in practical applications.