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A three-pole superconducting wavelength shifter (SWLS) cooled by a 1.5 W @ 4.2 K Gifford-McMahon cryocooler will be installed in SRRC's storage ring in the year 2002 to provide the synchrotron radiation light source with critical energy at 9 keV. This article shows the mechanical structure design of the cryogen-free SWLS. The three pairs of coils are supported in an aluminum-reinforced block and bonded by two iron return yokes. The poles are fixed to the return yoke and will move with the yoke. The finite element method is used to evaluate the stresses caused from the thermal contraction of materials and the coil's Lorentz force. The simulation result shows that the thermal stress of coil from 293 K to 4.2 K is too large and will cause the failure of the coil if the poles, the coils, and the aluminum support are all fixed together. The stress level is not reduced even the soft material is placed among the interfaces of these different parts. The reduction of the stress level is achieved by leaving a suitable clearance among these interfaces and allowing relative sliding motion between the return yoke and the coil, and between the coil and the aluminum support. Analysis results show that such a design will reduce the stress to a level of two to three times less.