Using the method of matched asymptotic expansions, the interaction between axisymmetric laminar boundary layers and inviscid supersonic external flows is investigated in the limit of large Reynolds numbers. The resulting triple-deck equations are solved numerically for two different cases of body shapes: a cylinder-cone configuration and a configuration consisting of two concentric cylinders which are connected by a smooth curve. Solutions to the linearized as well as the fully nonlinear equations are presented.