A multi-body dynamic rigid-flexible coupling model of landing gear is established to study the gear walk instability caused by the friction characteristics of the brake disc. After validating the model with the experimental results, the influence of the landing gear structure and braking system parameters on gear walk is further investigated. Among the above factors, the slope of the graph for the friction coefficient of the brake disc and the relative velocity of brake stators and rotors is the most influential factor on gear walk instability. Phase trajectory analysis verifies that gear walk occurs when the coupling of multiple factors causes the system to exhibit an equivalent negative damping trend. To consider a more realistic braking case, a back propagation neural network method is employed to describe the nonlinear behavior of the friction coefficient of the brake disc. With the realistic nonlinear model of the friction coefficient, the maximum error in predicting the braking torque is less than 10% and the effect of the brake disc temperature on gear walk is performed. The results reveal that a more negative friction slope may contribute to a more severe unstable gear walk, and reducing the braking pressure is an effective approach to avoid gear walk, which provides help for future braking system design.