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In this paper, an elastic-plastic deformation of a centrally heated two-layered composite cylinder with free ends subjected to uniformly distributed internal energy generation within an inner cylinder is studied using Tresca’s yield condition and its associated flow rule. Stress, strain and displacement distributions in the composite cylinder made of elastic-perfectly plastic material are derived considering the influence of geometric parameters as well as material properties such as yield strength, modulus of elasticity, Poisson’s ratio, coefficient of thermal conduction and coefficient of thermal expansion. Yielding starts at the outer boundary or at the axis corresponding to an ‘edge regime’ of Tresca’s prism in both cases. Propagations of the plastic regions are studied due to an increase of a heat generation.