A theoretical discussion is given of the propagation of weak hydromagnetic discontinuities (e.g., weak shocks) in an infinitely conducting, perfect, compressible fluid. The undisturbed flow is assumed to be steady and isentropic. As in geometrical optics, the wave fronts evolving from a given initial manifold‐there will be six of them, in general‐are constructed by means of rays. In addition, formulas are derived describing the variation of the discontinuity ``strength'' of a given propagating mode along rays associated with that mode. These results are employed to obtain an explicit solution of a simple mixed initial, boundary‐value problem that has been designed to illustrate, (1) a method of producing hydromagnetic disturbances, and (2) the fact that an initial disturbance gives rise, in general, to several propagating waves.