The mechanical properties of the uranyl squarate monohydrate material, [Formula: see text], were studied using theoretical solid-state methods based in density functional theory employing plane waves and pseudopotentials. Very demanding calculation parameters were utilized in order to obtain a realistic description of the mechanical behavior of this material. Since the determination of the positions of the hydrogen atoms in the unit cell of uranyl squarate monohydrate was not possible from x-ray diffraction data by structure refinement, they were fully optimized theoretically. The computed lattice parameters, bond distances, angles, and x-ray powder diffraction patterns of this material were in very good agreement with the experimental data. This material was found to be mechanically and dynamically stable since the corresponding stability conditions were satisfied. The values of the bulk modulus and its pressure derivatives, shear and Young moduli, Poisson ratio, ductility, hardness, and mechanical anisotropy indices of this material were reported. Furthermore, this study showed that this material exhibits the important negative Poisson ratio (NPR) and negative linear compressibility (NLC) phenomena. Uranyl squarate monohydrate is a very anisotropic brittle material characterized by a bulk modulus of ~33 GPa, which shows a minimum value of the NPR of the order of -0.5. Besides, this material displays NLC values for a limited range of positive pressures, from 0.025 GPa to 0.094 GPa, applied along the direction of minimum negative Poisson ratio. The analysis of the crystal structure as a function of pressure demonstrates that the mechanism of NLC of this material is associated to the change in shape of the uranyl pentagonal bipyramids and unrelated to the wine-rack structural mechanism commonly used to rationalize this phenomenon.