The method provides an improved quartz glass body, especially an improved quartz glass crucible for melting non-metals, non-ferrous metals, or silicon. The quartz glass body is made by a method in which a quartz glass-water mixture is supplied to a gypsum casting mold comprising an outer part and an inner part, dried in the gypsum mold, and put under an overpressure via a system of ducts in the form of textile tubes embedded in the mold during the drying. Later a resulting green glass body is removed from the mold. At least a portion of the shaping surfaces of the inner part of the gypsum mold are surfaces of a water-impermeable substance. The method provides a cast body with a reduced tendency to crack and with a smaller open porosity.