Standard higher order finite elements often perform unsatisfactory in contact problems. The major difficulties are caused by uneven distribution of nodal forces resulting in oscillating contact pressures. The paper presents a new approach that eliminates this drawback. The weight functions are chosen in such a way that even distributions of nodal forces are obtained. It is achieved by applying piece-wise linear functions. Two new 2D isoparametric quadratic elements are derived: 6-node triangle and 8-node quadrilateral, and tested in many examples. The new elements have unsymmetric stiffness matrices, but the provided examples show their good performance in contact problems