The stoichiometric MpXq hollow nanospheres are produced by reaction of metallic M nanospheres with the gaseous X phase. In the first stage a sufficiently thick MpXq nanoshell on the metallic core of phase M is formed. During this stage high supersaturation of vacancies in the M core or very high hydrostatic stress in the M core, due to the misfit between the core and the nanoshell, are developed and provide favourable conditions for the hollow nucleation. The misfit is caused by the Kirkendall effect. Based on the application of the thermodynamic extremal principle a kinetic model of MpXq nanoshell formation is derived. The kinetics is driven by the change of the chemical energy due to reaction of M and X components, of the interface and surface energies, and of the elastic strain energy due to misfit strain of the whole system. The model is used for simulation of the Cu2O shell growth kinetics due to oxidation of a Cu nanosphere, and the results of simulations are discussed.