Dynamical stability of solitary wave propagation in inhomogeneous cylindrical shell was numerically studied in detail by using method of integrating factors. Stable propagation keeping structure of waveform and propagation speed of solitary wave for long time was examined, under three kinds of initial perturbations that is Gaussian wave perturbation, harmonic wave perturbation and stochastic perturbation. It shows that stable propagation of solitary wave is related to amplitude, width and wavelength of perturbations. Only with small enough amplitude, width and wavelength, solitary wave shows relatively strong anti-interference property, and has better dynamical stability.