The structural, mechanical and lattice dynamical properties of Ru2B3 and Os2B3 have been investigated by using a first-principles method based on the density functional theory within the generalized gradient approximation. The single crystal elastic constants are numerically estimated using strain-stress approach. The polycrystalline aggregate elastic parameters are calculated from the single elastic constants via the Voigt-Reuss-Hill approximations. Subsequently, the ductility and brittleness are characterized with the estimation from Pugh's rule (B/G) and Cauchy pressure. Additionally, the Debye temperature is calculated from the average elastic wave velocity obtained from bulk and shear moduli. The calculated parameters are consistent with the previous experimental and theoretical data. These borides are both mechanically and dynamically stable in the considered structure.