Rough machining of a glass-ceramic material article such as a radome is accomplished using a high-power Nd:YAG laser. The radome is rotated about its longitudinal axis, and the point of application of the laser beam is translated generally parallel to the longitudinal axis over either the inside or outside surface of the radome. The Nd:YAG laser preferably operates in a pulsed wave mode with a pulse duration of from about 0.3 to about 3 milliseconds, a pulse frequency of from about 50 to about 500 pulses per second, and a pulse intensity of at least about 3.times.10.sup.4 Watts per square centimeter. After laser rough machining, at least about 0.002 inches of material is removed from the rough-machined surface by a finish machining, preferably mechanical grinding.