Abstract: A tubular core for carrying yarn wound therearound to define a bobbin for a textile machine, and method of making such core are provided, wherein the core has a load-carrying structure and an inside portion which is adapted to be engaged by a carrier shaft to provide substantially frictional holding of the core and bobbin on the shaft and wherein such inside portion comprises a sleeve made of a yieldable resilient polymeric material which is adapted to be yieldingly compressed between the structure and at least parts of the shaft to provide the frictional holding of the core in an improved manner and the yieldable resilient material of the sleeve enables the core and bobbin to be driven on the shaft while keeping such core substantially intact as well as enabling damage-free removal thereof to thereby define a reusable core.