Production of a laser‐produced plasma plume off a metallic target is accompanied by a strong shock wave with shock Mach number in excess of 100. Time‐resolved spectroscopy and streak photography show that the shock front evolves from a cylindrical to a complex profile. Along the beam axis the shock speed remains constant initially and then sharply increases due to a movement of the shock epicenter. Radially but close to the surface, the shock speed decays as r−0.5, where r is the distance from the laser beam axis. The observed behavior is consistent with the notion that the plasma plume grows toward the laser beam and becomes supercritical shortly after the peak of the laser pulse.