The site preference and thermodynamic properties of UTxAl12-x (T = Zr, Nb, Mo and Fe) and their related hydrides are studied based on the pair potentials obtained by the lattice inversion method. The calculated result demonstrates that the stabilizing elements Zr, Nb, or Mo prefer to substitute for Al in 8i sites; and Fe atom preferentially substitutes for Al in the 8f site. The interstitial H atoms only occupy 2b interstitial sites in UTxAl12-x. The calculated lattice parameters coincide with the experimental values. In addition, the total and partial phonon densities of states are first evaluated for these compounds.