In this paper, comparisons of the design optimization of ball grid array packaging geometry based on the elastic and viscoelastic material properties are made. Six geometric dimensions of the packaging are chosen as input variables. Molding compound and substrate are modeled as elastic and viscoelastic, respectively. Viscoplastic finite element analyses are performed to calculate the strain energy densities (SED) of the eutectic solder balls. Robust design optimizations to minimize SED are carried out, which accounts for the variance of the parameters via Kriging dimension reduction method. Optimum solutions are compared with those by the Taguchi method. It is found that the effects of the packaging geometry on the solder ball reliability are significant, and the optimization results are different depending on the materials modeling.