A new type of elastic coupling was designed with Monel metal corruated pipe.The coupling does not use key. The torque is transferred depending on the friction between spindle and hole. Compare key coupling with the elastic coupling ,the spindle s diameter can be produced by 30 percent ,and the moment of inertia is less than key coupling' s. The simple structure is convenient for production and fixation. We calculated the rigidity and intensity of the bolt and made a choice of bolt,and ,calcuated the intensity of the strain sheath and made certain the material for the new type of elastic coupling of Monel metal corrugated pipe. Also ,we calculated the rigidity and intensity of the metal corrugated pipe and made a choice for the material. Then. we made certain the link mode between metal corrugated pipe and strain sheath etc.