This paper deals with the simulation of nonlinear vibration induced by friction in an aircraft braking system. Experimental tests reveal that in similar experimental conditions the mechanism can generate vibrations of various amplitudes. The aim of this study is to simulate the behavior of the brake by taking into account the dispersion of parameters, which produce the variability of the response. A nonlinear model of the brake is presented. The time-history response is obtained by integration of the full set of nonlinear dynamic equations. Based on experimental results, the dispersions of the coefficient of friction and of the damping configuration are introduced. Monte Carlo simulations are performed and show a very good agreement with the experimental results.