Results of numerical simulation of supersonic gas flow past a blunt fin mounted on a flat plate with developing laminar boundary layer are presented. The calculations cover flow cases with the freestream Mach number of 6.7 and three different Reynolds numbers. A detailed analysis of flow characteristics such as temperature and surface heat flux are presented. In the smaller Reynolds number case, solution is steady-state and agrees very well with known numerical and experimental data. In case of larger Re values, the flow becomes periodic. These regimes are characterized by self-excited non-linear oscillations with almost the same fundamental frequency.