High thermal efficiency of Compact Heat Exchangers (CHX) makes them distinctly utile for application to Next Generation Nuclear Plants (NGNPs). The high temperature application and transient conditions of NGNP operation induce stresses in CHX. These induced stresses can be categorized under different classifications based on their cause and location. ASME Sec. III Div. 5 has different analysis methodologies based on failure modes, failure criteria to be assessed, and constitutive relationship considered. The primary objective of this study is to provide a description of the classification of stresses in CHX. Further, evaluation of CHX design is conducted according to simplified analysis methodologies in ASME Sec. III Div. 5: Elastic and Simplified Inelastic Analysis. These simplified analyses are performed following the submodeling technique. At the global level, the channeled core is replaced by an elastic orthotropic core for analysis. At the local level, the stresses and strains for critical regions are determined following the simplified analysis methods. The load controlled stresses are checked against HBB-3220 of ASME Sec. III Div. 5. For the Elastic Analysis Method, strains in critical sections in CHX are checked for thermomechanical cycle against the HBB-T-1320 of ASME Sec. III Div. 5 criteria. For Simplified Inelastic Analysis, critical sections are analyzed for strain limits following HBB-T-1330 of ASME Sec. III Div. 5. The analyses outcomes are compared and results are discussed.