In this paper, the effect of strain rate has been considered in the simulation of forming process with a simple form combined into the material law. Quite a few researchers have proposed various hardening laws and strain rate functions to describe the material tensile curve. In this study, the strain rate model Cowper-Symonds is used with anisotropic elasto-plastic material law in the simulation process. The strain path evolution of certain elements, when the strain rate is considered and not, is compared. Two sheet materials, Cold-reduced Carbon Steel (SPCC) JIS G3141 and Aluminum alloy 6112 are used in this study. Two yield criteria, Hill 48 and Hill 90, are applied respectively to improve the accuracy of simulation result. They show different performance when strain rate effect is considered. Strain path of the elements in the fracture risk area of SPCC (JIS G3141) varies much when the strain rate material law is used. There is only little difference of the strain distribution of Al 6112 when the strain rate effect is included and excluded in the material law. The simulation results of material SPCC under two conditions indicate that the strain rate should be considered if the material is the rate-sensitive material, which provides more accurate simulation results.