Abstract: A new mechanical model for FEM analysis of contact problems ispresented, in which a nodal point on the surface of contact body comes into contact with an arbitrary point on the surface of target body instead of the nodal point pair model. It is convenient to construct FE nets. The boundary conditions such as stick slid with friction and open contact were given in terms of this model. The contact boundary conditions as Lagrangian multipliers are substituted into the functional according to the principle of modified potential energy and therefrom the symmetrical nonlinear governing equations are deduced for the static and dynamic contact problems with material and/or geometric nonlinearities. Due to the symmetrization of equations, the general effective solution methods of nonlinear equations can also be used to the contact governing equations. In the paper the judgement criteria of contact conditions after each iteration are presented, which can decide whether and how the contact conditions of each contact nodal point to be modified.