The transient flow mathematical model of arbitrary shaped heterogeneous reservoir is constructed in this paper. In order to solve this model, perturbation method is employed and the solution is expanded into a series in powers of perturbation parameter. By using the boundary element method and Duhamel principle, wellbore pressure with effects of skins and wellbore storage is obtained. The type curves are plotted and analyzed considering effects of heterogeneity, arbitrary shape and impermeable barries. At last, the perturbation boundary element method is verified against the analytical solution and is applicable to transient pressure analysis of arbitrary shaped reservoir.