A shaped body of amorphous silicon dioxide, which has a chemical purity of at least 99.9% and a cristobalite content of at most 1% and which is impermeable to gas, is known. To provide shaped bodies of amorphous silicon dioxide which have a high precision, which can be small or large in size and of simple to complicated shape, which have a chemical purity of at least 99.9%, are impermeable to gas above wall thicknesses of 1 mm, which have a high cold flexural strength, low thermal conductivity and low radiation of heat, which are thermal shock resistant and can be exposed repeatedly or also long-term to temperatures in the range from 1000.degree. to 1300.degree. C. and which can be welded in a sharply delineated manner without spreading joins and which have a low spectral transmission from the ultraviolet to the middle infrared spectral region, the shaped body is opaque, contains pores, at a wall thickness of 1 mm has a direct spectral transmission which is virtually constant in the wavelength range from .lambda.=190 nm to .lambda.=2650 nm and is below 10%, and it has a density which is at least 2.15 g/cm.sup.3. A process for producing such shaped bodies is also provided.