An analytical model based on Tresca's yield criterion and its L associated flow rule is developed to analyze the thermoelastoplastic response of a linearly hardening cylinder subjected to a nonuniform heat source and convective heat transfer condition at the external boundary. Closed form solutions are obtained for a state of generalized plane strain in different stages of elastic-plastic deformation. Considering a cylinder that is constrained axially, the plastic deformation commences at the axis and depending on the convective boundary condition, another plastic region may develop at the surface before the fully plastic state is reached. A calculation procedure is developed to determine the critical values of the heat-transfer coefficient, for which a third plastic region at the surface does not occur. The effect of various parameters on the critical heat-transfer coefficient is investigated. The residual stresses attained upon unloading are also determined and it is shown that the primary and secondary stresses fall within the shakedown regime.