Abstract: According to the finite element method with effect of an axial force, the dynamic stability is presented for crane’s telescopic booms under a periodic load, which means a parametric resonance problem. Based on the Lagrange equation, the parametric vibration equation of stepped columns with small deformation under a periodic load is established; then the critical frequency equations of the telescopic booms’ dynamic instability region are derived; finally, the effect of damping to the dynamic stability of telescopic boom is discussed. The results show that efficient and accurate results for structures consisting of stepped columns can be yielded by using the presented method to analyze dynamic stability. As is demonstrated in the numerical examples, the dynamic instability regions are reducing when the damping coefficient increasing, and it affects more obviously to the second dynamic instability region.