Plane simple compression waves of finite amplitude are studied as they propagate into a fluid medium of constant state. Shock formation and subsequent expansion, as well as rise and decay of shock strength, are determined from a boundary‐value problem of mixed type involving a fixed boundary (source) and a moving boundary (shock surface). At the source, an overpressure is arbitrarily prescribed as a function of time; at the shock surface, the simple wave solutions are shown to satisfy the exact shock‐transition conditions within an accuracy including second powers of shock strength, while the shock speed is determined precisely. Shock speed and rise and decay of shock strength are shown to be strongly dependent on the particular form of the overpressure generated at the source in the course of time. Approximation formulas are derived for weak shocks and are used in a detailed discussion of two examples.