Transition-metal light-element compounds are potential candidates for hard materials. In the past, most of studies focused on the binary transition metal borides, carbides and nitrides, while the researches of ternary phases are relatively rare. In this paper, the structure units of the known Nb₃B₃C and Nb₄B₃C₂ phases are first analyzed to be Nb₆C octahedron and Nb₆B triangular prism, respectively. By stacking the Nb₆C octahedron and Nb₆B triangular prism, twenty ternary Nb-B-C and twenty ternary Ta-B-C configurations with different compositions are constructed. The chemical formula of these Nb-B-C and Ta-B-C configurations can be defined to be Nb_{(m + n + 2)}B_{(2m + 2)}C_n and Ta_{(m + n + 2)}B_{(2m + 2)}C_n, respectively. Using first-principles density functional calculations, thermodynamical, dynamical and mechanical stabilities of the constructed ternary Nb-B-C and Ta-B-C configurations are investigated through calculating their enthalpies of formation, phonon dispersions and elastic constants. Five Nb-B-C (Nb₃B₃C, Nb₄B₃C₂, Nb₆B₄C₃, Nb₇B₄C₄ and Nb₇B₆C₃) phases and six Ta-B-C (Ta₃B₃C, Ta₄B₃C₂, Ta₆B₄C₃, Ta₇B₄C₄, Ta₇B₆C₃ and Ta₃BC₂) phases are predicted to be stable by analyzing the constructed ternary Nb-B-C and Ta-B-C phase diagrams, in which the seven phases (Nb₆B₄C₃, Ta₃B₃C, Ta₄B₃C₂, Ta₆B₄C₃, Ta₇B₄C₄, Ta₇B₆C₃ and Ta₃BC₂) are first predicted to be stable. The Nb₆B₄C₃, Ta₆B₄C₃, Ta₄B₃C₂ and Ta₃B₃C phases are stable when temperature is higher than 1730, 210, 360 and 1100 K, respectively. And the Ta₃BC₂ phase is stable only when temperature is lower than 130 K. The calculated results about mechanical and electric properties show that these Nb-B-C and Ta-B-C phases are conductive materials with a high hardness in a range of 23.8–27.4 GPa.