This paper presents some research results obtained recently in using the p-version of the finite element method (FEM) for shape optimal design. It is shown that the p-version 2-D elastic element can be extended to employ part of a Bezier or B-spline curve as its element side. This new element has been tested successfully with the patch test. Moreover, it is compatible, has no preferred direction, and contains all the required rigid body modes. Preliminary results of some classical shape optimal design problems indicate that optimal shapes can be obtained with fewer degrees of freedom when compared to the h-version FEM. As with the h-version, ten iterations are sufficient for the convergence of the optimization process in most of the problems.