A method for calculating decay rates of vibrational modes in large polyatomic systems is proposed and tested. The high frequency excited vibration is treated quantum mechanically, and the soft modes are described classically. The initial state is described by the hybrid quantum/classical self-consistent-field (SCF) approximation. The formalism is based-on a golden-rule expression. The driving potential is the difference between the full Hamiltonian and the mean field Hamiltonian (SCF) causing the decay of the initial state to final mixed quantum/classical ;SCF states. These states are calculated using an extension of the usual static mean-field techniques to systems with mixed quantum and classical degrees of freedom. The formalism for obtaining the mean-field states and calculating the decay rates is presented, and the method is applied to a diatomic molecule treated quantum mechanically, embedded in a 1D model for a. rare gas cluster treated classically. The dependence of the eigenenergies of the quantum and the decay rates with temperature is studied. The influence on the system size is also presented and compared with the prediction of the isolated binary collision model. The effect of a change in the linear density of the cluster on the eigenenergies of the vibrational mode is presented.