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In the present work, we have investigated the structural, electronic, elastic, and thermodynamic properties of transition‐metal boron‐carbon compounds (TMBCs) (TM = Ti, Zr, Hf) using the first‐principles calculations. The results showed that TMBCs are energetically and thermodynamically stable, and the sequence of phase stability is HfBC > ZrBC > TiBC. B‐C bonds can be formed in TMBCs ceramics due to the strong hybridization between B‐2p and C‐2p states. The elastic anisotropies of TMBCs were illustrated by elastic anisotropy indexes, 3D surface constructions, and 2D projections, and the results indicated that the sequence of elastic anisotropy is ZrBC > TiBC > HfBC. Finally, the calculated minimum thermal conductivities, based on the Clarke's and Cahill's models, of all TMBCs are anisotropic with the sequence of ZrBC > TiBC > HfBC.

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