Using the first principles full potential linearized augmented plane wave (FLAPW) method and the pseudopotential plane wave (CASTEP) method, the elastic constants of Fe-based magnetic cubic phases are investigated. The key point is confirmed to be the lattice constants when calculating elastic constants, and the basis sets also affect the precision of calculation. More precise results were got by FLAPW. The elastic constants C11, C12, C44 of bcc-Fe are 283 GPa, 158 GPa and 112 GPa, respectively，which approximately consist with the intrinsic ones. The elastic constants C11, C12, C44 of Fe-Ga magnetostrictive material are calculated to be 207 GPa, 166 GPa and 108 GPa, respectively.