Major simplifications of the corresponding rigorous thermal and thermo-mechanical analyses are applied in this chapter. Transient temperature fields are replaced by fixed temperature profiles. The 'computationally efficient' (CE) methods introduce further simplifications where transverse and longitudinal thermal strains are derived from approximations embodied in the mismatched thermal strain and transverse contraction strain algorithms. In the CE 'analytical' approach, these strains are applied to linear elastic, small strain models, using conventional strength of materials techniques. In the CE 'computational' approach, the strains are applied to linear-elastic, large-strain, finite-element models. Various hybrid stepwise methods are also shown, where a measure of sequential description is included, together with the use of elasto-plastic, finite-element computation.