In previous paper non-stationary streamlining of a blunt body by a supersonic flow with a finite-length thin rarefied channel on its axis was considered. Now analytic and numeric treatment is expanded on the case of infinite discontinuity. Both supersonic and subsonic conditions inside a channel are described in unique approach. The approach is applicable also for the description of a sharpen body - wedge as the simplest representative - interaction with mentioned discontinuity type. The stationary gas dynamic geometry turned out to be independent on the body shape. The shock detachment criterion is formulated - detachment occurs if interaction with discontinuity leads to diminishing of the shock angle, and simultaneously the pressure after the shock. Foundation for such assumption is confirmed by numeric calculations. Reduction of a sharpen body drag at a fixed portion demands deeper rarefaction of gas in a channel than in the case of blunt body. The dependencies of shock detachment velocity on the dimensionless density in the channel for blunt body and wedge are obtained. Comparison with experimental values manifests in favor of highly non-uniform structure of MW plasmoid. The product of three parameters define the ultimate efficiency of interaction - the ratio of cross-sections of body and discontinuity, the square of undisturbed flow Mach number and the body aerodynamic performance. In spite of the last parameter can be small, the first two parameters are large, the fact that gives foundation to assume the method of drag reduction by means of MW energy deposition in supersonic flow as beneficial.