Abstract: The parametric variational principle is established for the static problem with different modulus in tension and compression. Based on the parametric variational principle and finite element method, the 2-D bimodular static problem is transformed into a linear complementarity problem that can be solved by using Lemke’s algorithm. The method doesn’t need the pre-assumption of the stress state and the update of the stiffness matrix. Numerical examples show that the proposed method is stable and significantly accelerates the convergence of solution.