Abstract <p>A closed mathematical model of continuous spin detonation of a syngas—air mixture is stated in a three-dimensional unsteady gas-dynamic formulation, and an algorithm for numerically solving the problem is developed. The model is verified using experimental data on ignition delay at high temperatures and the results of one-dimensional numerical calculations of the Chapman–Jouguet detonation parameters. For three stoichiometric compositions in an annular cylindrical combustor 306 mm in diameter, single-wave continuous spin detonation modes are obtained and the three-dimensional structure and the main flow parameters are analyzed. The minimum possible flow rates for continuous detonation are obtained in the case of variable specific mixture flow rates in a range of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(90{-} 260\)</EquationSource> <!--CESW2570024Simonov-m1--> </InlineEquation> kg/(s m²). The resulting data are compared with existing experimental data</p>