Delayed coking as a part of heavy oil upgrading is characterized with severe thermal–mechanical operating conditions. Coke drums operating under such conditions require proper design and material selection in order to sustain the high stresses caused by the thermal–mechanical loading. This paper has the objective to explore alternative material selections for coke drum applications based on material property data provided in ASME Boiler & Pressure Vessel Code, Section II—Materials. The materials were compared based on the stress levels obtained by using finite element analyses (FEA) for two critical loading scenarios in the coke drum operation cycle, i.e., the heating up and quenching stages. The results show that closer matching in the coefficients of thermal expansion (CTE) between clad and base materials reduce significantly the stress in the clad during heating up stage. Among other material properties, the results show that the variation in Young's modulus values of base materials plays an important role in the variation of maximum stress in the coke drum shell during the bending of the shell caused by quenching water. Among the considered 11 pairs of clad and base material combinations, the combination of SA302-C as the base material and nickel alloy N06625 as the cladding material is recommended for delayed coke drum application.