Abstract: The double nonlinearity including both surface nonlinearity and constitutive nonlinearity will appear in elasto-plastic contact problem with friction. In this patter, a mixed formulation for finite element contact analysis combined with Newton-Raphson iterative procedure, axe used to solve this kind of problem and the Fortran program for this procedure is also listed. After being checked by some illustrative examples, it is used to analysis the elasto-plastie be havior of heavy-duty spur gears in mesh. All the results have shown the validity and versatility of this method.