We report precision micromachining of fused quartz and Pyrex glass by laser-induced plasma-assisted ablation (LIPAA) using a conventional nanosecond UV or visible laser. High- quality micrograting structures with periods of 1.06 and 20 micrometers using a phase mask and a mask projection technique, respectively were fabricated by LIPAA. The Fresnel zone pattern was also produced in fused quartz. The hole with the size of 700 micrometers in diameter was fast drilled in fused quartz and Pyrex glass. A possible ablation mechanism was discussed based on the dependence of ablation metal target and glass substrate.