The Wendelstein 7-X (W7-X) optimized stellarator is presently under construction at the Max-Planck-Institut für Plasmaphysik in Greifswald. The goal of W7-X is to verify that the advanced stellarator magnetic confinement concept is a viable option for a fusion reactor. The W7-X coil system consisting of 70 superconducting coils of seven different types is supported by a massive central support structure (CSS), and thermally protected by the cryostat. The magnet system's weight is borne by supports (cryo-legs) which are bolted to the cold CSS. They reach down through the cryostat wall to the warm machine base which means that a small thermal conductivity is important to keep thermal losses at an acceptable level. Therefore, the design of the cryo-legs incorporates glass-reinforced plastic (GRP) tubes which are shrink-fitted into stainless steel flanges at the ends. In order to ensure free thermal shrinkage of the magnet system and to reduce stresses in the cryo-legs, sliding and rotating bearings are used as interfaces to the machine base. Tie rods between the machine base and the warm ends of the cryo-legs prevent toroidal movements of the magnet system with respect to the torus axis. Nevertheless, significant deformation of the CSS during operation results in tilting of the cryo-legs in such a way that toroidal movements of the whole magnet system take place. The number of cryo-legs and their stiffness are chosen such that the toroidal movement is kept within an acceptable range. All these restrictions, as well as requirements concerning simplicity and ease of assembly, make the cryo-leg design and structural analysis quite a complex and challenging task. The paper presents an overview of structural analyses of the W7-X magnet system with cryo-legs, local analyses of a cryo-leg under design loads, and FE simulation of the cryo-leg mechanical test.