In this article the p-version finite element method is applied to finite strain problems. In particular, the behaviour of high order finite elements is studied for an isotropic hyperelastic material in the case of near incompressibility. The question of robustness with respect to distortion and efficiency of anisotropic p-version elements for thin-walled or beam-like structures will be addressed. It will be shown that the p-version finite element approach is a promising method to compute geometrically highly non-linear structures. (C) 2003 Elsevier B.V. All rights reserved.