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We present the results of experimental and numerical investigations of the structure of the supersonic M = 3 flow past an arrangement of a semicone on a flat plate, where the cone vertex coincides with the supersonic leading edge of the plate. Using a specially developed optical method for visualizing supersonic conical flows it is established that in the flow past the arrangement at zero or nonzero angle of attack the separation region arising on interaction of either the conical bow shock or the inner shock wave with the plate boundary layer is situated totally on the plate. The appearance of additional singular lines on the semicone surface and vortex structures of inviscid origin in the shock layer is due to the occurrence of contact discontinuities proceeding from the triple points of either the λ-configuration of shock waves accompanying the separation region on the plate or the bow shock wave arising in the flow past the arrangement with or without an angle of attack. Numerical codes for calculating the flow in the conical approximation are developed basing on the viscous and inviscid gas models. The comparison of the calculated results with experimental data shows their satisfactory agreement and possible usage domains of any of these approaches.