The purposes of the paper are to consider the failure phenomenon by delamination and crack when the encapsulant of plastic IC package under hygrothermal loading in the IR soldering process shows elastic and viscoelastic behaviors and to suggest the optimum design by the approaches of stress analysis and fracture mechanics. The model for analysis is the plastic Small Outline J-lead package with a dimpled diepad. On the package without a crack, the stress analysis is done and the possibility of delamination is considered. For the model fully delaminated between the chip and the dimpled diepad, -integrals in low temperature and -integrals in high temperature are calculated for the various design variables and the fracture integrity is discussed. Finally, the optimal values of design variables to depress the delamination and crack growth in the plastic IC package are obtained.