To provide a method for polishing of a glass substrate, capable of improving the flatness of the polished glass substrate, and to apply the polishing method to a cleaning method for the glass substrate.

According to the polishing method for the glass substrate, a main surface of the glass substrate is polished by moving a fluid containing grains harder than the glass substrate 4 and the main surface relative to each other at high speed along a direction in which the main surface of the glass substrate 4 extends. According to the cleaning method for the glass substrate, the glass substrate 4 is cleaned by moving a fluid containing grains softer than the glass substrate 4 and the main surface relative to each other at high speed along the direction in which the main surface of the glass substrate 4 extends.