A stability analysis of the mass spectrum indicates that hadrons, like atoms and nuclei, are shell-structured. The mesonic shells mass series, combined with the results of a mass quantization analysis, reveals striking similarities with the nuclear shells. In addition, the mesonic mass patterns suggest solid-phase partonic bound states on an fcc lattice, compatible with a model by A. O. Barut with stable leptons as constituents, bound by magnetism. Baryonic shells grow with a lower density, and only start at shell 3 with the nucleon.