Friction stir welding is a solid-phase welding process based on the mixing of the pasty material in the stirred zone. The main advantage of this technique is the ability to weld metal alloys which are generally difficult to weld by conventional welding processes. In this paper an analytical model is proposed for the description in 2D the distribution of the material (fluid) flow in the vicinity of the tool pin during friction stir welding process "FSW". For this reason, the analytical solutions are built on the basis of traditional problem of mechanics of the fluids which is used to solve the equation associated with this problem. Furthermore, the aim is to make an analytical study of these aspects for a better understanding of this phenomenon. This method provides a reduction in computational time compared to those required for finite or differential elements methods. Moreover, it highlights on the effects of the different parameters on the material flow during welding.