The contact algorithm based on Riemann solution was used to simulate the penetration process of high velocity impact problems in two-dimension axisymmetric coordinates. The artificial viscosity hadn't been used when the velocities and stresses at the contact surface were determined by Riemann solution instead of the mean values of velocities and stresses between the contacting basic and surrounding particles. It shows the achieved result is the same as FEM, and the method can be applied in impact problems.