The spin Hamiltonian of the hyperfine interaction between a shallow donor and the Si29 nuclei has been derived on the basis of the effective mass wave function. The interference effect between the Bloch functions of different valleys is shown to be largely responsible for the anisotropy of the electron-nuclear hyperfine interaction. An expression for the resonance frequency was derived in the high field approximation. The theory is shown to account for the experimental observations of Feher on the anisotropic hyperfine interaction quantitatively. The coefficient of the 2p core function in the OPW conduction band edge Bloch functions has been determined by comparison with Feher's results to be 0.20 approximately. It is pointed out that on the basis of the theory given, the positions of the conduction band minima and the anisotropy of the donor effective mass wave function can be precisely determined by the method of ENDOR and its pressure effects.