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Coupled thermal and mechanical design issues in a high power light emitting diode (LED) package platform are investigated using numerical models. A thermal resistance network model and a 3-D finite element model are built for thermal and stress analyses. They are validated with the experimental data and subsequently utilized to study the effect of key parameters on the junction temperature and the thermal strains. An extensive parametric analysis is conducted to assess the effect of design and material parameters on the junction temperature and thermal strains of the high power LED under study. Based on the results, the desired parameters of adhesives for high power LED applications are identified and an example of an LED thermo-mechanical design protocol is presented.