Abstract: An improved sleeve construction for mandrels of the type which grip tubular members such as paper rolls by selectively expanding a rubber or other deformable material sleeve into gripping relation with the inner wall surface of the tubular members wherein the sleeve is sealed at the opposite ends thereof to the mandrel shaft and air is introduced against the inner wall of the central portion of the sleeve to expand it. The sleeve itself is tubular in shape and formed of a rubber material with alternating portions of arcuately long, radially thick, dimensionally stable, first segments separated by arcuately short, radially thin, dimensionally deformable, second segments. The short thin segments are expanded responsive to the introduction of air against the inner wall thereof while the longer, thicker segments include an outer surface which is moved into gripping relation with the tubular members responsive to expansion of the second segments.