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Applying external strain is an efficient way to manipulate the site preference of dopants in semiconductors, however, the validity of the previous continuum elastic model for the strain influence on the doping forma- tion energy is still under debate. In this paper, by combining quantum mechanical theoretical analysis and first-principles calculations, we show that if the occupation change of different orbitals caused by the strain is negligible, the continuum elastic model is valid, otherwise it will fail. Our theory is confirmed by first-principles calculation of Mn-doped GaAs system. Moreover, we show that under compressive strain the hole density, thus the Curie temperature TC can increase in Mn-doped spintronic materials., Comment: 4 pages + 2 figures