A KdV-like equation describing wave propagation in microstructured solids as a governing equation, the dynamical stability of solitary waves propagating in microstructured solids was numerical simulated using the method of integrating factors. Using Gaussian wave, Ricker wavelet and Hyperbolic secant wave as initial disturbance, the stable propagation property of solitary wave keeping the waveform and propagation speed for a long time was investigated, under the three different small disturbances. The simulation results show that different small disturbances have different effects on solitary wave, the stable propagation of solitary waves is related to the amplitude and width of the disturbance. Only under disturbances of very small amplitude and width, the solitary waves can exhibit a certain degree of anti-interference and dynamical stability, and can stably propagate in microstructured solids for a long time.