The mechanical and thermodynamic properties of α-UH3 under pressure have been examined by first-principles pseudopotential plane-wave calculations based on the density functional theory. In order to describe the strong on-site Coulomb repulsion among the localized 5f electrons, the generalized gradient approximation and local density approximation plus a Hubbard parameter (GGA + U and LDA + U) formalisms have been adopted for the exchange correlation term. The pressure evolution of elastic constants of α-UH3 has been revealed, and α-UH3 is found to be mechanically stable at least up to 20 GPa. Under pressure, the low-frequency vibration modes of α-UH3 change slightly, while the high-frequency vibration modes shift upward. Our study is expected to facilitate the understanding of uranium hydrides and their applications.