A procedure for constructing the three-dimensional viscoelastic constitutive model of polymeric packaging material over a wide range of temperatures is presented. By using both tensile and torsional dynamic mechanical analyses (DMA) and thermal mechanical analyses (TMA), the viscoelastic constitutive behavior of a low-filler-percentage epoxy molding compound (EMC) was first characterized. Storage modulus mastercurves obtained from the DMA were converted to the relaxation moduli in the Laplace-Carson transform domain. The transformed Young's and shear relaxation moduli were then curve fitted by using an optimization procedure with restriction for ensuring physically admissible time-dependent Poisson's ratio. Bulk and shear relaxation moduli were then obtained from the fitted moduli and inverse transformed to the time domain. A numerical finite element model that considers the viscoelastic constitutive behavior of EMC was applied to simulate warpage of an overmolded flip-chip package under the surface mount solder reflow process and compared to experimental shadow Moiré measurements for validating the constitutive model.