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Transition metal borides as Mo₂FeB₂, Mo₂NiB₂, and WCoB have recently caught attention because they exhibit excellent mechanical properties for wear resistant applications. On the other hand, it is widely known that the addition of Cr and/or Mo as alloying elements improves the mechanical properties and corrosion resistance of some alloys. In this investigation, first principles calculations were performed to study the structural properties of the ternary B₂Cr_1-xMo_x within DFT formalism. The B₂Cr_1-xMo_x compounds were studied for a concentration x of 25%, 50%, and 75%. The Minima Hopping method was used to search over the stable and metastable structures for each concentration. B₂Cr_1-xMo_x structures were optimized to obtain the lattice parameters, total energies and formation enthalpies in each case. The elastic constants were calculated to verify the mechanical stability of the compounds, as well as the bulk modulus, shear modulus, Young’s modulus, and Poisson’s Ratio. The mechanical strength of the ternary was maximized as a function of the alloying concentration. Free energies were also calculated to study the thermal stability of the found crystal phases.