There is considerable uncertainty in the prediction of performance of a system, due mainly to idealizations in geometry, material behavior, and loading history. Uncertainties in geometry can be predicted and controlled using tighter tolerances. However, the models currently used to describe material behavior are mostly deterministic. To predict the coupling efficiency of a photonic system to a greater degree of confidence, stochastic analysis procedures are necessary. As part of such an analysis, the behavior of materials must be stochastically characterized. In this paper, we present extensive experimental data on thermally and UV-cured epoxies, typically used in photonic packages to enable stochastic analysis. We perform dynamic mechanical analysis over a wide frequency and temperature range to determine the viscoelastic behavior of the epoxies. We next derive an analytical description of the time-dependent behavior of a vertical cavity surface emitting laser (VCSEL) array bonded to a substrate. We further characterize the variation in the displacement of the VCSEL array due to the stochastic, viscoelastic behavior of the bond epoxy. We carry out Monte Carlo simulation to predict the uncertainty in the coupling efficiency of a generic photonic package. We finally relate the size of the VCSEL laser array to its ability to achieve the required coupling efficiency.