Abstract : The numerical simulation of contact problems is still a delicate matter especially when large transformations are involved. In that case, relative large slidings must be taken into account between the contact surfaces and the discretization error induced by linear finite elements may not be satisfactory. In particular, linear elements lead to a facetization of the contact surface, meaning an unavoidable discontinuity of the normal vector to this surface. Uncertainty over the precision of the results, irregularity of the speed on the contact nodes and even numerical oscillations are the consequences of such discontinuity. Among the different methods developed in order to fix this problem, one may be interested in studies carried out using mortar formulations. Other authorsproposed to create a C1-continuous surface based on the initial mesh in order to optimize the detection of penetrations. Finally, work published in the area of biomechanics about the numerical simulation of mammographies considered C1-continuous Hermitte finite elements. In the present paper, we focus on these last two methods. They are combined with a finite element code using the bi-potential method to manage contact. We restrict our study to 2D contact problems for which we use 3 or 4-noded linear finite elements.