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This study addresses an existing gap in the literature by providing a comparative analysis of various adhesive model representation approaches, using cohesive zone models—both local and continuum models. Through a systematic investigation of stress distribution and force–displacement characteristics across different modeling techniques, we reveal the advantages and limitations of each method. This study provides a comparison of various adhesive modeling approaches, including single-row cohesive elements, interfacial elements, middle cohesive elements, and single-row continuum solid elements, highlighting their effects on stress distribution and failure modes in single lap joints across a range of adherend thicknesses and overlap lengths. The findings demonstrate that the choice of modeling techniques yields a similar prediction of failure modes in single lap joints under tensile loading. Consequently, choosing among these methods can be guided by the level of detail in capturing localized damage mechanisms. The results offer a foundation for informed decision making in adhesive modeling, with implications for improving joint design and reliability in real-world applications.