Using the logarithmic hoop strain，a nonlinear dynamic equation governing the axisymmetric radial motion of an axially compressed cylindrical shell subjected to radial disturbance is derived. By means of Bubnov-Galerkin approach the partial differential equation can be transformed into an ordinary differential equation containing second-order nonlinear term. The qualitative analysis indicates that the autonomous dynamic systems corresponding to two cases of pre-buckling and post-buckling has the form-same homoclinic orbits and two orbits locate different positions on the horizontal axis of phase plane. The threshold condition for the occurrence of Smale horseshoe-type chaos in disturbed system is obtained by Melnikov’s method. Finally, the bifurcation diagram, time-history curve, phase portrait and Poincare’s map are calculated.