Abstract: This paper deals with elastic contact problems, which belongs to category of boundary condition nonlinearity with small deformation. The nonlinearity of elastic contact problems is due to the contact conditions of the points contacted.The mixed approach suggested by this paper are suited for solving the local nonlinear problems. The general ideas of this mixed approach using F.E.M are as following; after the discretion of elastic bodies, according the displacement field assumed, we can get the stiffness matrix of elastic bodies, thus the matrix of influence coefficients of contact stress at the contacting boundaries can be determined, further more regarding the contact stresses as unknown variables, the compatibility conditions at contact boundaries then were given. As a matter of fact, we thus performed a procedure which localized the nonlinearity of the problem.The computational result shows that to solve such class of problems with complex nonlinear boundary conditions by means of this method, the computational speed and storage are slightly greater or approach to those in solving general linear problems.