The elastic constants, elastic modulus, anisotropy, Debye temperature, and sound velocity properties of Mo0.85Nb0.15B3 were investigated by first-principles calculations under pressure based on the generalized gradient approximation (GGA) proposed by Perdew–Burke-Ernzerhof (PBE). Employing the stress-strain method and the Voigt-Reuss-Hill approximations, were calculated the elastic properties of single and polycrystalline crystals; Bulk modulus (B), Young modulus (E), Poisson ratio (ν), Pugh ratio (G/B), Debye temperature and the Cauchy pressure terms. The calculated ν, Cauchy pressure, and Pugh ratio G/B values indicate that Mo0.85Nb0.15B3 shows a transition from brittle to ductile under pressure. Finally, the Density of States decreases as pressure increases.