Much research has been carried out to realize through-silicon via (TSV) technology for three-dimensional (3D) chip stacking packaging. A vertical chip interconnection method using Cu/Sn-Ag bumps and nonconductive films (NCFs) is one of the most promising approaches for 3D TSV vertical interconnection. In this work, the relationship between the viscosity of pre-applied NCFs and loading forces was investigated to predict the gap change between a TSV chip and a substrate chip. Existing theories of squeeze flow are adapted to predict the gap change of a real TSV chip and a substrate chip during TSV bonding using a simplified model. The real gaps measured during bonding of test dies were matched to check the validity of the prediction model. Considering the thixotropy of NCFs, the prediction well matched the real gap changes between bumped TSV chips and substrate chips during bonding.