Self-assembling protein nanocontainers are promising candidates for an increasingly wide scope of purposes. Their applications range from drug delivery vehicles and imaging agents to nanocompartments for controlled enzymatic activity. In order to exploit their full potential in these different fields, characterization of their properties is vital. For example, their mechanical properties give insight into the stability of a particle as a function of their internal content. The mechanics can be probed by atomic force microscopy nanoindentation, and while this single particle method is increasingly used to probe material properties of viral nanocages, it has hardly been used to characterize nonviral nanocages. Here we report nanoindentation studies on two types of nonviral nanocontainers: (i) lumazine synthase from Aquifex aeolicus (AaLS), which naturally self-assembles into icosahedral cages, and (ii) the artificial protein cage O3-33 originating from a computational design approach. In addition, we tested particles that had been engineered toward improved cargo loading capacity and compared these nanocages in empty and loaded states. We found that the thermostable AaLS cages are stiffer and resist higher forces before breaking than the O3-33 particles, but that mutations affecting the size of AaLS particles have a dramatic effect on their structural stability. Furthermore, we show that cargo packaging can occur while maintaining the cage's mechanical properties.