Disclosed are systems for scoring non-flat materials including non-flat glass sheets (1000). In one embodiment, a laser scoring system is described. The laser scoring system includes a laser (102) and an optical head (106). The optical head is configured to receive output from the laser and focus the output into an elongated laser beam having a beam waist and an extended focal depth (116) of greater than +/- 5 mm relative to the center of the beam waist with a power density sufficient for scoring a material having at least a portion within the extended focal depth. In one aspect the system can include a beam expander (104). The beam expander receives the output from the laser, expands the output from the laser to an expanded laser beam, and transmits the expanded laser beam to the optical head.