We carried out the three-dimensional (3-D) mechanical design of a 2-m-long 20 T common-coil dipole magnet and provided solutions for coil stress management. Instead of using flared ends to make space for the beam pipe, the prototype magnet is designed with a coil configuration which consists of four Nb 3 Sn and six Bi-2212 flat racetrack coils. The designed peak coil field is 20.4 T at the operating current of 14 700 A. The operating margin is 11% on the load line at 4.2 K. The magnitude of the calculated Lorentz force for 1/8 model is around 1562, 405, and 206 t for the horizontal, vertical, and axial directions, respectively. The special coil configuration and such significant magnetic force bring unprecedented challenges in applying preload to coils and optimizing the coil stress and the stress in the other components. By using an extended aluminum shell and a split yoke assembly, we minimized the coil end effects and applied a uniform and large enough preload to the coil straight section and the coil ends. This paper presents the stress analysis and the optimized 3-D mechanical design of the magnet.