We have studied the mechanical properties and phonon dispersions of fully hydrogenated borophene (borophane) under strains by first principles calculations. Uniaxial tensile strains along the a- and b-direction, respectively, and biaxial tensile strain have been considered. Our results show that the mechanical properties and phonon stability of borophane are both highly anisotropic. The ultimate tensile strain along the a-direction is only 0.12, but it can be as large as 0.30 along the b-direction. Compared to borophene and other 2D materials (graphene, graphane, silicene, silicane, h-BN, phosphorene and MoS2), borophane presents the most remarkable anisotropy in in-plane ultimate strain, which is very important for strain engineering. Furthermore, the phonon dispersions under the three applied strains indicate that borophane can withstand up to 5% and 15% uniaxial tensile strain along the a- and b-direction, respectively, and 9% biaxial tensile strain, indicating that mechanical failure in borophane is likely to originate from phonon instability.