The elastic-plastic deformation of a tube subjected to radially uniform heat generation is considered using Tresca's yield function, its associated flow rule, and a linear work-hardening law. The tube is assumed to be in the state of plane strain and all the elastic and thermal parameters are taken to be temperature independent. For a uniform heat source Q, which increases monotonically with time and which has an insulated inner surface, yielding commences at the inner boundary and propagates outward upon further thermal loading. Immediately after initiation of yield, a plastic region (inner) and an elastic region (outer) are formed with the tangential stress as the intermediate principal stress in both regions. The maximum strength of a heat source, QM, to which a tube may be subjected is taken to correspond to that value of Q which makes the tube almost entirely plastic. This value of Q is computed for several graphite tubes of different thicknesses and then compared with an experimentally obtained QF which corresponds to total failure (fracture) of these tubes. A value of approximately 2.5 is obtained for QF/QM for tubes of moderate thicknesses. Furthermore, the ratio QF/QM remains practically constant as tube thickness increases. Agreement between theory and experiment especially in depicting the dependence of failure load on tube thickness and temperature gradient is considered excellent in light of the many assumptions made. The application of this theory to the design of nuclear reactor fuel elements is also pointed out.