A model of reactive hot pressing of zirconium carbide (ZrCx, 0.5 < x < 1) has been constructed that incorporates four processes that occur in parallel: creep of zirconium (Zr), reaction of Zr and carbon (C), increase in volume fraction of hard phase with progressive reaction that reduces the creep of Zr and, finally, de-densification associated with volume reduction during reaction. The reasonable agreement of the model with experimental results verifies that plastic deformation of Zr is the main factor that is responsible for the low-temperature reactive densification of ZrC and that ZrC may be treated as a rigid inclusion that contributes little to densification. It predicts that densification is impaired by increasing carbon stoichiometry due to the increasing amount of starting hard phase and the greater contraction upon reaction. Additionally, the model predicts that mixtures of Zr and ZrC should show equal or better densification than Zr and C mixtures.