The work presents results of the modeling of a three-dimensional rotation detonation engine combustion chamber; the chamber is supplied with a hydrogen–oxygen mixture. The chamber cross-section shape is annular. To model the processes in the chamber, a computer program was created incorporating a mathematical model for multi-component gas dynamics with chemical transformations, turbulence, and external energy sources. An elementary chemical kinetic mechanism and a high-order accuracy numerical model were used. Different modes of fuel and oxidizer supply, and three types of the combustible mixture: rich, lean, and stoichiometric, were investigated. Cases for additional air or oxygen supply from orifices at the lateral walls were studied. Several modes of stable detonation, single wave or multiple waves, were obtained, for a stoichiometric mixture with additional oxygen supply, for a rich mixture with additional oxygen, and for a lean mixture with additional air. For those cases, the fuel and oxidizer fluxes and the thrust characteristics were analyzed.