Thermal stress distributions in uniform circular cylindrical shells due to axial temperature distributions are investigated. The discontinuity effect due to the presence of a cooler stiffening bulkhead is considered, and the possibility of thermal buckling of the shell due to the circumferential discontinuity stress is examined. The buckling analysis is based on Donnell's shell equation, and particular attention is given to shells having clamped edges. An experimental investigation of this buckling problem is discussed, and the results obtained are seen to agree reasonably well with theory.