A laser machining system and method uses a shaped laser beam, such as a long, narrow beam, and effectively scans the beam in the narrow direction across a mask having an aperture pattern. The pattern on the mask is imaged onto a moving workpiece and the patterned laser beam selectively removes material from the workpiece. The workpiece may be moved using a coordinated synchronized rotational motion. The laser may use a longer wavelength (e.g., 248 nm) and the beam may be scanned at a high rate of speed to reduce the dissipation of the residual thermal energy in the material being machined. In one embodiment, this system and method may be used to machine a complex pattern into a curved surface with relatively high resolution and high speeds.