Vacuum assisted resin transfer molding (VARTM) is a liquid composite molding (LCM) technique to manufacture large scale composite structures. Fiber preforms are placed on a tool surface and covered by highly permeable layer known as the distribution media to enhance the flow in the in-plane direction. The assembly is enveloped in a plastic bag and a vacuum draws the resin into the preform through the distribution media. Woven and stitched preform architecture contain tightly packed fiber tows which have much lower permeability as compared to the bulk permeability of the fabric. Thus, the tows saturate with resin much later than the pores between the fiber tows and are more prone to microvoid creation, which are detrimental to part performance. Numerical modeling can predict the fiber tow saturation, but it tends to significantly under-predict saturation in VARTM process as compared to experimental results. To improve the predictions one needs to model the post-filling stage in VARTM. After the injection is discontinued, the resin pressure will drop and increase the compaction pressure on the fabric and the distribution media. This will compress the distribution media forcing the resin into the fiber tows and towards the resin trap at the vent location. This post-filling flow has not been addressed in traditional filling simulations. The current work analyzes the resin flow from the collapsing distribution media into unsaturated fiber tows. First, the governing formulation is derived and conditions under which the mathematical model can be simplified are stated. Next, a simplified analytic solution is provided to determine the significant non-dimensional parameters that influence the post-filling process. Finally, the post-filling stage is added to a mold filling simulation package and the predictions of unsaturated fiber tows are found to be more in line with experimental observations.