The concept of hypervalency emerged as a notion for chemical bonding in molecules to explain the atomic coordination in hypervalent molecules that violates the electron-octet rule. Despite its significance, however, hypervalency in condensed phases, such as amorphous solids, remains largely unexplored. Using ab initio molecular-dynamics simulations, we report here the underlying principles of hypervalency in amorphous chalcogenide materials, in terms of the behaviour of hypervalent structural units, and its implicit relationship with material properties. The origin of a material-dependent tendency towards hypervalency is made evident with the multi-centre hyperbonding model, from which its relationship to abnormally large Born effective charges is also unambiguously revealed. The hyperbonding model is here extended to include interactions with cation s2 lone pairs (LPs); such deep-lying LPs can also play a significant role in determining the properties of these chalcogenide materials. The role of hypervalency constitutes an indispensable and important part of chemical interactions in amorphous and crystalline chalcogenide solids.