Results of numerical simulation of the supersonic gas flow past a fin-body mounted on the flat plate with developing laminar boundary layer are presented. The calculations cover flow cases with the freestream Mach number of 6.7 and two different Reynolds numbers: Re=12500, 15600. The structure of the horseshoe vortices arising in the body leading-edge region is analyzed. It has been revealed that for both the Reynolds numbers there exist two stable solutions, which correspond to different metastable states of the flow. The solutions differ in the number of the vortices forming in the separation region, as well as in the separation region length. In the smaller Reynolds number case, both solutions are steady-state, whereas in case of the larger Re value, one of the solutions remains steady-state, and the other one becomes quasi-periodic.