Thermal stress and displacement equations are derived for an internally clad tube for which the ratio of cladding thickness to internal tube radius is small with respect to unity and in which the cladding and the basic tube have different material properties. When the difference between the cladding temperature and the average temperature of the basic tube is large enough, plastic flow is found to occur in the cladding. The corresponding solution is found by making use of the Tresca yield condition and its associated flow law. The solution is examined to guide the designer in the selection of those cladding material properties that would delay the initiation of plastic flow.