Abstract: The traditional upper bound finite element method uses circumscribed polygons to approximate the Mohr-Coulomb yield circle. The calculation results are more accurate only when the number of polygon sides is sufficient，which often leads to the excessive scale of linear programming and slow convergence speed. It has a certain impact on engineering applications. So we relaxed the requirements that all the points must strictly meet the limit properties. The best uniform approximation polygon form was adopted to construct the linearized yield function and plastic flow equation. The numerical example showed that the method used could get a precise result by less number of polygon edges，and could greatly improve the convergence speed.