A circular cylindrical elastic fibre has a concentric coating of elastic-plastic material which obeys Tresca's yield condition and associated flow rule. Theoretical solutions are given for the uniform extension of the composite cylinder; both infinitesimal and finite extensions are considered. The unloading and subsequent reloading of the cylinder are also analysed. The problem is of interest in connection with the mechanics of fibre-reinforced metals. Numerical results are given for an aluminium-silica system. Good qualitative agreement with experiment is obtained.