For the gear system with flexible couplings, the nonlinear elastic force and damping force are both the functions of displacement and velocity. A nonlinear stochastic system is generated under the excitation of stochastic force. The path integral method based on GaussLegendre integral is applied to calculate the joint probability density of displacement and velocity responses. Moreover, the distributions of probability density at some special time points are given. In the end, the problem of probability loss is analyzed, and a feasible measure to deal with it is also put forward.