An arc tube and method of fabricating the arc tube for a discharge lamp. The arc tube includes an arc tube main body 10 at which a sealed glass bulb 12 serving as a discharge portion sandwiched by pinch seal portions is formed at a portion of a glass tube W along the longitudinal direction thereof, and a cylindrical shroud glass 20 which is welded on and integrated with the arc tube main body 10 so as to cover the sealed glass bulb 12, the front and rear end portions of the shroud glass 20 may be joined, for example, by welding on shroud glass welded portions with circular cross sections provided at the front and rear end sides of the arc tube main body 10, respectively. The inner peripheral surface of the diameter reduced portion of the shroud glass tube 20, which is molten, soften and deformed inside along the radial direction, contacts closely to the circular outer peripheral surface on the arc tube main body 10 side, so that a space can not be formed at the welding portion of the shroud glass 20 (adhesion surface). Thus, the atmosphere does not enter into the sealed space 24 surrounded by the shroud glass 20, and accordingly, devitrification is prevented.