First-principles calculations were performed to investigate the structural, electronic and phonon properties of MoTa and MoNb in the CsCl (B2) phase. The calculated lattice constants, static bulk modulus and first-order pressure derivative of the bulk modulus are in good agreement with available experimental data and previous theoretical predictions. Electronic band structures and partial and total densities of states have been derived for MoTa and MoNb. The band structures show metallic character; the conductivity is mostly governed by Mo-4d and Ta-5d (Nb-4d) states. A linear-response approach to the density functional theory is used to derive phonon dispersion curves and the density of states for MoTa and MoNb. Zone centre optical phonon modes of MoTa and MoNb are found to be at 6.46 and 7.24 THz, respectively.