Cold spray is a process which is used in coating industry and manufacturing of new parts. Experimental studies of this process are expensive and also very difficult due to high velocity of particles. Therefore, one effective method to study this process is its computer simulation. Previous works show that the Johnson-Cook hardening law has been usually used for simulation of this process. However, it is unanimously believed that this model is not able to reproduce the material behavior at extremely high strain rates commonly occurred in the cold spray process. Therefore, the simulation results are expected to improve if a suitable material model for extremely high strain rates is used. In this study, the PTW1 model was implemented in ABAQUS commercial finite element package. The cold spray process was then simulated for copper using both the PTW and Johnson-Cook hardening models. A comparison between the simulation and experimental results showed that the PTW model did improve the simulation results. The predicted flow stress by Johnson-Cook model was also shown to be not so sensitive to strain rate at extremely high strain rates.