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This article describes an analytical model for the prediction of the underfill flow characteristics in a flip-chip package driven by capillary action. In this model, we consider non-Newtonian fluid properties of the encapsulant as opposed to most other studies where Newtonian fluid properties were assumed for the underfill flow. The power-law constitutive equation was applied in our study. The simulation based on this model agreed well with the measurement obtained from the experiments available in literature. It was further shown that this model performs better than the Washburn model traditionally used for the prediction of underfill flow characteristics in the flip-chip packaging. Based on this model, the effects of the solder bump pattern (including bump pitch, solder bump diameter, and gap height) on the process variables (i.e., flow front and filling time) were studied, which facilitated both the package design and the process optimization.