A quartz material is subjected to heat-contact treatment with ammonia gas at 1200 DEG C or below in the presence of a carbon-producing source with rapid and easy formation of a silicon oxynitride coating (layer) on the surface of the quartz material. The surface-treated quartz material obtained has excellent heat resistance, and detachment of the silicon oxynitride coating from the quartz material does not occur, even if the latter is subjected to repeated heating cycles. Furthermore, the heat resistance is further improved if a second surface-treatment step is carried out with application of a silicon nitride film to the silicon oxynitride coating using a CVD process or the like after the surface-treatment step with formation of a silicon oxynitride coating on the surface of the quartz material.
