We report first-principles calculations of ideal tensile and shear strength for the recently synthesized orthorhombic OsB2 that is a primary example of a new class of ultra-hard materials synthesized by combining small, light, and covalent elements with large, electron-rich transition metals. Our calculations show that the shear strength on the (001) plane is highly anisotropic with a low peak stress of 9.1 GPa in the (001)[010] shear direction but a much higher peak stress of 26.9 GPa in the (001)[100] direction. The strong resistance against (001)[100] shear deformation prevents the indenter from making a deep imprint, giving rise to a high Vickers hardness on the (001) plane, despite the weak shear strength in the (001)[010] shear direction. The calculated peak stress of 26.9 GPa in the (001)[100] shear direction agrees well with the 30 GPa Vickers hardness observed experimentally on the (001) plane in OSB2. However, the weak shear strength (9.1 GPa) in the (001)[010] shear direction severely limits its application as abrasives and cutting tools for ferrous metals as well as scratch-resistance coatings. Our results highlight the importance of understanding atomistic deformation modes under various loading conditions in designing new ultra-hard materials.