In the paper, results of numerical simulation of a shock-wave pattern and vortex structures forming in supersonic flow past an adjacent-to-plate elongate cylindrical body, which penetrates the developing flat-plate boundary layer, have been presented. The laminar flow regime at Mach number 2.95 was considered, Reynolds number was taken 4000. The solutions were obtained using two schemes for convective flux (HLL and AUSM). Comparison of the flow fields calculated with the mentioned schemes of the first and second orders of accuracy were conducted. Solution grid sensitivity issues were discussed.