Abstract This paper presents some research results obtained recently using the p- version of the finite element method (FEM) for shape optimal design. The use of Bezier and B-spline curves to define design elements has proven to be an excellent way to model the geometry of the design problem. The p- version 2D elastic element was extended to employ part of a Bezier or B-spline curve as its element side for this purpose. 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 (three zero eigenvalues are found in the element stiffness matrix). There are several advantages in using the p- version FEM for shape optimal design. The analysis and design models are often identical. In the p- version FEM, the stresses along an element side are as accurate as those inside the element. This feature is important because usually the critical stress constraints are found along the design element boundary. The final design can very easily be reanalyzed with a different element order to check the accuracy of the result. Some classical shape optimal design problems have been solved using the Conlin optimizer. The results indicate that similar optimal shapes can be obtained with fewer degrees of freedom than when compared with the h- version FEM. As with the h- version , less than ten structural analyses are sufficient for convergence in most of the problems.