Density functional (B3LYP) method with Relativistic Effective Core Potential (RECP) have been used to optimize the structures and to calculate the potential energy function both for the ground and excited states of UH and UH2 molecules. Results show that the ground state of UH and UH2 molecules are X4Π and X3A2, which belongs to C2v symmetry, and the disassociation energies are 2.886 eV and 5.249ev respectively, and the spectral data of UH and UH2 have also been derived both for the ground and excited state. The potential energy functions of UH and UH2 have been derived based on normal equation fitting method and the many-body expansion theory. The information is useful to mechanism analysis of the aging effect of the hydrogen storage material.