Heteroepitaxial thin films of cubic silicon carbide (3C-SiC) on silicon offer a promising platform for leveraging the properties of SiC, such as wide bandgap, high mechanical strength, and chemical stability on a silicon substrate. Such heteroepitaxial films also attract considerable interest as pseudosubstrates for the growth of GaN as well as graphene on silicon wafers. However, due to a substantial lattice mismatch, the growth of 3C-SiC on silicon leads to a considerable amount of stresses, defects, and diffusion phenomena at the heterointerface. We show here that the extent of such interface phenomena and stresses is so large that, after patterning of the SiC, a massive sublimation of the silicon underneath the SiC/Si interface is promoted via a high-temperature anneal, either in high or medium vacuum ambient. A micrometer-thick air gap can be formed below the SiC structures, making them suspended. Hence, the described approach can be used as a straightforward methodology to form free-standing silicon carbide structures without the need for wet or anisotropic etching and could be of great interest for devices where suspended moving parts are needed, such as micro- and nanoelectromechanical systems.