This paper presents a new analytical filling time model to predict the flow of non-Newtonian underfill fluid during flip-chip encapsulation process. The current model is formulated based on the regional segregation approach, instead of the conventional porous media approximation. In this approach, the filling times were computed separately at different filling stages, before being summed up till the required filling distance. The non-Newtonian property of underfill fluid is modeled using the conventional power-law constitutive equation. Additionally, the spatial aspects of the underfill flow were incorporated into the present analysis. For instance, the evolution of underfill menisci from convex to concave was analytically developed and the contact line jump (CLJ) criterion was improved using minimal flow assumption. Upon validated with three distinct past underfill experiments, the current analytical model is found to have the best performance as it predicted the filling times with the least discrepancy among other existing filling time models. Quantitatively, the discrepancies were averagely reduced by an absolute value of at least 8.68% and 4.90%, respectively, for the first two set of validation studies. Generally, this model is particularly useful in manufacturing lines to estimate the process time of flip-chip underfill, as well as for the optimizations of process and package design.