Using ab initio calculations, the effects of uniaxial, biaxial, and hydrostatic strains on the magnetocrystalline anisotropy of $L1_0$-orderd FePt and CoPt alloys were systematically investigated. Interestingly, the rates and the signs of magnetocrystalline anisotropy changes of FePt and CoPt were determined by the directions and dimensions of strains. The calculation results are consistent with the previous experimental observations and are expected to provide directions to tailor magnetic properties of various types of $L1_0$-ordered FePt and CoPt systems.