We present a study of structural, elastic and thermodynamic properties of tetragonal (C11_b) U₂Mo by means of density-functional theory based calculations using full-potential linearized augmented plane wave method. In this approach the generalized gradient approximation were used for the exchange-correlation potential calculation. The optimized lattice parameters are in excellent agreement with the experimental data. Through the Debye-Grüneisen model the temperature and pressure dependence of equation of state, bulk modulus, thermal expansion and specific heat have been obtained and discussed in the range of pressure 0.20 GPa and the temperature 0.800 K.