In order to provide method and apparatus for manufacturing a vitreous silica crucible with little mixing of foreign matter and stable arc during arc melting, the method and apparatus for manufacturing a vitreous silica crucible have a device which blows off air from the side of arc electrodes toward a melting space of a mold, and air discharge ports which discharge the air within the heating furnace, and perform forced supply of air into the melting space during melting to make the atmospheric pressure of the melting space higher than the surroundings, and preferably, form an air pressure difference of 100 Pa or more between the melting space and the surroundings, thereby performing melting.