Rate-dependent constitutive model was used to simulate the friction stir welding process. The effect of the viscosity coefficient and the process parameters on the material behaviors and the stress distributions around the pin were studied. Results indicate that the stress in front of the pin is larger than that behind the pin. The difference between the radial/circumferential stress in front of the pin and that behind it becomes smaller when the material gets closer to the top surface. This difference increases with increasing the viscosity coefficient and becomes smaller when the welding speed decreases. The variation of the angular velocity does not significantly affect the difference.