Coke drums are critical equipment in the petroleum industry. The failure modes of coke drums include excessive bulging deformation and fatigue cracking. The elastic-plastic behavior of a coke drum, subjected to both thermal and mechanical loadings, is analyzed for a complete cycle of operation. The effects of multiple operational cycles and localized hot/cold spots are also investigated. It is found that yielding of the clad layer starts at the very early stage in an operating cycle and permanent deformation is caused in the first operating cycle. Plastic shakedown occurs in the clad layer under combined operating thermal and mechanical loadings. It is also found that both hot and cold spots will cause bulging of the shell and the cold spot can cause more severe deformation than the hot spot.