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)[100] 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.