An implicit iterative algorithm, based on the continuous moving least square (CMLS), is developed to simulate material mixing in Friction Stir Welding (FSW) process. Strong formulation is chosen for the modeling of the mechanical problem in Lagrangian framework to avoid the drawback of numerical integration. This algorithm is well adapted to large deformations in the mixing zone in the neighborhood of the welding tool. We limit ourselves to bidimensional viscoplastic problem to show the performance of the proposed implicit algorithm. The results show that the proposed algorithm can be employed to simulate FSW.