Abstract: The solution of 3D elastic-plastic frictional contact problems belongs to the unspecified boundary problems where the interaction between two kinds of nonlinearities should occur. Considering the difficulties for the solution of 3D frictional contact problems, the key part is the determination of the tangential slip states at the contact points, and a great amount of computing work is needed for a high accuracy result. A new method based on a combination of programming and iteration methods, which are respectively known as two main kinds of methods for contact analysis, was put forward to deal with 3D elastic-plastic contact problems. Numerical results demonstrate the efficiency of the algorithm illustrated here.