Uranium trioxide (UO3) is a stable chemical form of uranium oxide with multiple polymorphs found throughout the nuclear fuel cycle. The pressure-induced changes in the structure and lattice dynamics of four of these polymorphs are simulated with density functional perturbation theory and analyzed. Two phases, α- and δ-UO3 are found to exhibit an isotropic response to pressure and do not undergo any changes in coordination geometry up to ∼40 GPa. In contrast, the other two phases investigated, β- and γ-UO3, exhibit an anisotropic response to pressure. Decomposition of the phonon eigenvectors allows us to assign specific pressure-induced structural changes to individual phonon modes. This analysis has been performed on a per atom basis for the relatively simple α- and δ-UO3 structures, which have one symmetrically unique uranium site, and on a per coordination environment basis for β- and γ-UO3, which have multiple U sites.