Using finite element simulation software Deform-3D, the material flow traits and principle during cross wedge rolling (CWR) process were simulated and combined with the physical simulation and production in practice, the reasons that cause concaves in the both sides of the billets in CWR process were analyzed. The method to avoid the concaves was brought forward by using taper billet, and the influence of the taper's dimension on the side concaves was studied. The simulation results show that the side concaves can be decreased and even eliminated by using billets with cone-shape sides, and the depth of the concave decreases with the decreasing of tape angle. The side of the workpeice is almost flat without concaves when the tape angle is 120°.