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A double stator symmetrical type multi pump and multi speed motor is designed based on the principles of existing symmetrical constant pumps and constant motors. In the shell, a rotor is corresponding to two stators, so the multi speed motor can work independently and synchronously. As an example, we describe the structure and working principle of the double acting symmetrical type double stator multi speed motor, define its symbolic representation method, and analyze the output flow features of the multi pump and the output speed and torque features of the multi speed motor. The speed of the multi speed motor under different combinations of multi pump and multi speed motor is analyzed. The results show symmetric type double stator multi speed motor can output many different speeds and torques. The study establishes a basis for applications of double stator multi pump and multi speed motor system on machine tools, mobile machineries and so on.