Abstract In this paper, with the assuption of effective lattice mode of coupling, a generalized theoretical expression of multiphonon relaxation rate has been derived by using quantum mechanical generating function method. An analytical rate expression is presented for high-order approximation case. Limitations of relaxation rate expressions in weak coupling approxamation given by Fong et al. with the quantum statistical method, and in weak coupling approximation and low temperature approximation given by Miyakawa et al. with quantum statistical method are pointed out. The dependence of the multiphonon relaxation rate on temperature, phonon. energy, energy gap and displacement parameter are also calculated.