A numerical modeling of a swirling turbulent jet in a coflowing stream was carried out. The flow description involved two second-order mathematical models. The first one includes the averaged equations of motion and the differential equations for transfer of normal Reynolds stresses and dissipation rate in the thin shear layer approximation. The second model relies on the far wake approximation. The distances from the source of the jet in the calculations reached very large values. At small distances, the calculated profiles of the averaged velocity components agree well with the known experimental data from Lavrent’ev Institute of Hydrodynamics SB RAS. At large distances from the source, the flow becomes close to the self-similar one, with degeneration laws and normalized profiles consistent with the known theoretical concepts of the dynamics of swirling turbulent jets in a coflowing stream. The problem of asymptotic behavior of a nonswirling turbulent jet in a coflowing stream was also considered. A self-similar solution based on numerical experiments was obtained.