The numerical simulation results of the flow of a gas-liquid medium over the high-temperature metal cylinder surface in a circular channel are presented. The flow over the solid metal cylinder with a variable cross-section by a gas-liquid medium is considered. Based on the mathematical model taking into account the cooling-media-flow axial symmetry relative to the cylinder longitudinal axis, the results of the numerical simulation of the process of solving the two-dimensional nonstationary problem of the coupled heat exchange of the gas-liquid medium flow and metal cylinder are obtained. The control volume approach is used for solving the differential equation system. The flow field parameters are calculated using the algorithm SIMPLE. For the iterative solution of linear algebraic equations, Gauss-Seidel method with under-relaxation is used. The numerical calculation results are obtained for the flow hydrodynamic parameters of the gas-liquid medium at cooling the high-temperature metal cylinder by taking into account vaporization. The values of temperatures, flow velocities, and vapour distribution in the computational domain are determined. The variation intensity of the metal cylinder surface temperature depending on the gas-liquid flow velocity is analyzed.