Abstract: The Navier-Stokes equations for two-dimensional agitated flow in the polar coordinates are solved with the finite element method. The penalty function and integration reduction techniques were used in the finite element formulation to treat the incompressibility constraint of fluids and eliminate the pressure term in the momentum equation. The velocity distribution, flow patterns and shear - rate distributions were successfully calculated for the 2-D agitated flow field induced by an anchor impeller. The good agreement of the calculated flow patterns with those obtained experimentally indicated the reasonableness of the present treatment. Numerical simulation was further carried on for various values of Reynolds number, and the influence of Reynolds number on the agitated flow fields was discribed.