Friction stir welding is a new solid state joining technology, which is suitable for joining some hard-to-weld materials, such as aluminum alloy, magnesium alloy, etc. The modeling of material flows can provide an efficient method for the investigation on the mechanism of friction stir welding. So, 3D material flows under different process parameters in the FSW process of 1018 steel are studied by using rate-dependent constitutive model. Numerical results indicate that the border of the shoulder can affect the material flow near the shoulder-plate interface. The mixture of the material in the lower half of the friction stir weld can benefit from the increase in the angular velocity or the decrease in the welding speed. But flaws may occur when the angular velocity is very high or the translational velocity is very small. When the angular velocity applied on the pin is small or the welding speed is high, the role of the extrusion of pin on transport of the material in FSW becomes more important. Swirl or vortex occurs in the tangent material flow and may be easier to be observed with the increase in the angular velocity of the pin.