Abstract: It is common for many dynamical systems to have complex incursive fractal basin boundaries under external excitations. The purpose of this paper is to discuss the effect of noises on erosion of safe basin in the softening Duffing oscillator. By introducing the portrait of the system's safe basin briefly and employing the Runge-Kutta and the Monte-Carlo methods, the eroded safe basins are presented when the softening Duffing oscillator with or without damping item is excited by the Gaussian white or the bounded noise. It is shown that, similar to the case of determinate harmonic excitation, the area of the safe basin decreases with the increase of the strength of the stochastic excitation. The boundary of the safe basin also becomes incursive fractal when the damping item is absent and the system is excited only by the Gaussian white or the bounded noise.