A slender in-extensional cantilever model excited by this transverse pedestal moments with the form of the Gaussian white noise was studied. The purpose of this paper was to explore how the geometrical nonlinearity influence the responses of the model excited by the Gaussian white noise. The curvature nonlinearity and inertia nonlinearity problems were addressed emphatically. The standard stochastic averaging method was applied to simplify the system into the Ito functions of amplitude and

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... . Stationary probability density function (PDF) of amplitude, the joint PDF of the displacement and velocity together with the reliability function and the probability density of the first passage failure time were studied theoretically and numerically. The theoretical approximations coincide with the digital results very well when noise density is not too large. When the noise is stronger, a prediction-correction method was proposed to improve the predicting performance. Numerical simulations verified the effectiveness of this approach.