In the present paper, the dynamic stability of circular cylindrical shells is investigated; thecombined effect of compressive static and periodic axial loads is considered. The Sanders–Koiter theory is applied to model the nonlinear dynamics of the system in the case of finiteamplitude of vibration; Lagrange equations are used to reduce the nonlinear partial differentialequations to a set of ordinary differential equations. The dynamic stability is investigatedusing direct numerical simulation and a dichotomic algorithm to find the instabilityboundaries as the excitation frequency is varied; the effect of geometric imperfections isinvestigated in detail. The accuracy of the approach is checked by means of comparisonswith the literature.