The disclosed process includes making a slip or slurry by mixing alumina powder, water, a deflocculant and a magnesium compound, casting the slip or slurry by drain casting and thereafter firing or sintering same. A coagulant is used as the deflocculant.A tube for a lamp, which is a unitary body of translucent alumina ceramic, has a large-diameter portion located at a central portion of the tube and two small-diameter portions located at both end portions of the tube. The tube is produced by drain casting. The tube has substantially the same wall thickness over its whole length. The inner surface of the tube is more smooth than its outer surface.