In this thesis, a new method which minimizes the maximum joint torque of four legged walking robot is proposed. The maximum joint torque minimization is necessary to the prevention of excessive joint torque, miniaturization and lightness in weight of driving motors. Due to this minimization is accomplished with optimal distribution of reaction forces which act on feet, an additional freedom which is produced from a quadruped walking robot with standard crab gait is used to obtain optimal reaction forces which minimize the maximum joint torque. In addition, the redundancy is used to remove discontinuity of vertical reaction force of a walking robot. Simulation results show that the maximum joint torque is minimized and discontinuity of vertical reaction force is removed. Finally, a neural network shows that it makes possible to real time processing of this approach which consumes a tremendous processing time.