Results of a numerical study of the flow structure in the rectangular duct of a model air inlet with the interaction of the shock wave generated by the inlet cowl with the turbulent boundary layer on the inner duct surfaces are reported. A configuration involving a convergent entrance section and a constant-cross-section throat was analyzed. The numerical simulation of the three-dimensional flow with free-stream Mach number M = 4 was performed on the basis of the Reynolds-averaged Navier-Stokes equations and the k-ω SST model of turbulence. As a result of the calculations, the limit streamlines and the distributions of static pressure on the duct surfaces, as well as the distributions of total pressure and the fields of Mach number in duct cross sections were obtained. The structure of the flow is analyzed and the possibility of occurrence of longitudinal vortex structures in the corner region of the intake-duct throat is shown.