Results of a numerical study of supersonic flows formed in channels with a square cross section are reported. Configurations consisting of a constricting entrance section formed by four compression wedges aligned at a right angle to each other and a subsequent channel with a constant cross section are considered. The initial shock waves formed on the nose compression wedges pairwise intersect each other in dihedral corners of the configuration along the swept lines, and a complex system of reflected and subsequent interacting shock waves of the general three-dimensional position is formed further downstream. The data are obtained in a supersonic range of freestream Mach numbers M = 2–4 for compression wedge angles of 3° and 8° in flows with both regular and irregular interaction of the initial shock waves in dihedral corners of the configuration.