After budding from the host cell, retroviruses undergo a process of internal reorganization called maturation, which is prerequisite to infectivity. Viral maturation is accompanied by dramatic morphological changes, which are poorly understood in physical/mechanistic terms. Here, we study the mechanical properties of live mature and immature murine leukemia virus particles by indentation-type experiments conducted with an atomic force microscope tip. We find that both mature and immature particles have an elastic shell. Strikingly, the virus shell is twofold stiffer in the immature (0.68 N/m) than the mature (0.31 N/m) form. However, finite-element simulation shows that the average Young's modulus of the immature form is more than fourfold lower than that of the mature form. This finding suggests that per length unit, the protein-protein interactions in the mature shell are stronger than those in the immature shell. We also show that the mature virus shell is brittle, since it can be broken by application of large loading forces, by firm attachment to a substrate, or by repeated application of force. Our results are the first analysis of the mechanical properties of an animal virus, and demonstrate a linkage between virus morphology and mechanical properties.