Experimentally, U2Mo is known to exist in tetragonal structure at ambient conditions. In contrast to experimental reports, the past theoretical studies carried out in this material do not find this phase to be stable structure at zero pressure. In order to examine this discrepancy between experiment and theory, we have performed ab-initio electronic band structure calculations on this material. In our theoretical study, we have attempted to search for lowest enthalpy structure at ambient as well at high pressure up to 200 GPa, employing evolutionary structure search algorithm in conjunction with ab-inito method. Our investigations suggest that a hexagonal structure with space group symmetry P6/mmm is the lowest enthalpy structure not only at ambient pressure but also up to pressure range of ~200 GPa. To further, substantiate the results of these static lattice calculations the elastic and lattice dynamical stability has also been analysed. The theoretical isotherm derived from these calculations has been utilized to determine the Hugoniot of this material. Various physical properties such as zero pressure equilibrium volume, bulk modulus and its pressure derivative has also been derived from theoretical isotherm.