Yielding of two-layer shrink-fitted composite tubes with axially constrained ends subject to either internal or external pressure is investigated in detail. In the framework of small deformations, a state of plane strain and von Mises yield criterion, analytical expressions are obtained for critical values of the pressure leading to plastic flow. It is shown that, depending on material properties and tube dimensions, different modes of plastic deformation may occur. Yielding may commence at the inner tube or at the outer tube or simultaneously in both tubes. The conditions for different nature of plastic flow are determined. Using analytical expressions obtained for critical values of the parameters and properties of real engineering materials, various numerical examples are handled and the variation of elastic limit pressure with interference and interface radius is explained.