In this paper, the structure, hydrogen storage capacity, mechanical, electronic, optical and thermodynamic properties of hydride perovskites KCuH3 and RbCuH3 are systematically studied via using density functional theory (DFT) for the first time. The formation energies and mechanical properties of XCuH3 (X = K, Rb) hydrides indicate that KCuH3 and RbCuH3 are both thermodynamically and mechanically stable. The values of Pugh's index and Cauchy pressure for KCuH3 and RbCuH3 indicate that they are both brittle materials. In addition, their bonding types are mainly ionic bonds. Electronic properties show that these compounds are metallic. The hydrogen storage capacities of KCuH3 and RbCuH3 are calculated to be 2.78 wt% and 1.95 wt%, respectively. The optical properties indicate that KCuH3 and RbCuH3 both have high dielectric functions in the visible range and their absorption coefficient peak in the ultraviolet range. Additionally, the thermodynamic properties, including free energy, Debye temperature, melting temperature, entropy and heat capacity are calculated. The analyzed physical properties of KCuH3 and RbCuH3 perovskite hydrides suggest that they have great prospect in hydrogen applications. All the above parameters are calculated for the first time, which could contribute significantly to the development of sustainable energy technologies.