First-principles calculations were employed to study the mechanical properties for the recently proposed tetragonal B 4CO 4 ( t-B 4CO 4). The calculated structural parameters and elastic constants of t-B 4CO 4 are in excellent agreement with the previous results, indicating the reliability of the present calculations. The directional dependences of the Young’s modulus and shear modulus for t-B 4CO 4 are deduced in detail, and the corresponding results suggest that the t-B 4CO 4 possesses a high degree of anisotropy. Based on the strain-stress method, the ideal tensile and shear strengths along the principal crystal directions are calculated, and the obtained results indicate that the shear mode along (001) slip system dominates the plastic deformation of t-B 4CO 4, which can be ascribed to the breaking of the ionic B-O bonds. The weakest ideal shear strength of 27.5 GPa demonstrates that the t-B 4CO 4 compound is not a superhard material, but is indeed a hard material. Based on the atomic explanation that the ternary B-C-O compounds cannot acquire high ideal strength, we propose two possible routes to design superhard B-C-O compounds.