A coupling algorithm is used to compute the equilibrium of a flexible anchor impeller in a stirred vessel. This coupling algorithm is based on a partitioned approach, which consists of three relatively independent modules: the computational fluid dynamics (CFD), the computational structure dynamics (CSD) and the interface. In the CFD module, the Euler formulation was used to account for the moving boundary. In the CSD module, the updated Lagrangian formulation for solving the motion of non-linear structure was used and a static study was adopted. In the interface module, an exchange of the forces and displacements was allowed. The numerical results, such as the velocity field, the turbulent kinetic energy, its dissipation rate, the turbulent viscosity and the mechanical deformation, have been presented. Particularly, we are interested in the study of the static behavior of the anchor impeller and the evolution of the displacement field of the arms during various iterations of our coupling algorithm. Accordingly, if the anchor impeller undergoes a deformation due to the flexion of the arms of the anchor impeller, the numerical results changes slightly from iteration to another. At the end of certain iteration, the anchor impeller becomes deformed and the velocity field is preserved. These results confirm that the fluid has a significant effect on the deformation of the arms of the anchor impeller during mixing depending on the velocity of the anchor impeller and the fluid flow. The numerical results were validated by a comparison with literature data.