The properties of zone plates with different boundary shapes are considered. These shapes are discussed as special cases of the super ellipse. For each case the Fresnel-Kirchhoff diffraction integral is numerically evaluated. It is shown that an elliptical zone plate yields an astigmatic image with axial intensity peaks corresponding to the semi-major and semi-minor axes. In the case of the super ellipse, an additional peak proportional to the square of the diagonal length is obtained. The results were experimentally confirmed in the elliptical case.