Abstract: This paper utilizes two Laurrent’s series which satisfy the conditions of notraction on inner elliptical boundary,and sets up functions.It turns out that the otherboundary conditions can be satisfied provided that the variation of the functions equals zero.With the variational approaching,the elastic problem with void is resovled.Furthermore,this method is applied to the model of periodical distributed void,the effective modulus andthe effctive Poisson’s ratios have been obtained.