Capsid maturation with large-scale subunit reorganization occurs in virtually all viruses that use a motor to package nucleic acid into preformed particles. A variety of ensemble studies indicate that the particles gain greater stability during this process, however, it is unknown which material properties of the fragile procapsids change. Using Atomic Force Microscopy-based nano-indentation, we study the development of the mechanical properties during maturation of bacteriophage HK97, a λ-like phage of which the maturation-induced morphological changes are well described. We show that mechanical stabilization and strengthening occurs in three independent ways: (i) an increase of the Young's modulus, (ii) a strong rise of the capsid's ultimate strength, and (iii) a growth of the resistance against material fatigue. The Young's modulus of immature and mature capsids, as determined from thin shell theory, fit with the values calculated using a new multiscale simulation approach. This multiscale calculation shows that the increase in Young's modulus isn't dependent on the crosslinking between capsomers. In contrast, the ultimate strength of the capsids does increase even when a limited number of cross-links are formed while full crosslinking appears to protect the shell against material fatigue. Compared to phage λ, the covalent crosslinking at the icosahedral and quasi threefold axes of HK97 yields a mechanically more robust particle than the addition of the gpD protein during maturation of phage λ. These results corroborate the expected increase in capsid stability and strength during maturation, however in an unexpected intricate way, underlining the complex structure of these self-assembling nanocontainers.