This paper discusses the dynamic analysis of thin-walled composite shells under axial load. analytical and numerical methods are used to analyze and validate the results with experimental results has been made. In this paper effects of orthotropic of materials, boundary conditions, geometry, geometric imperfections and time course load on the linear and nonlinear analysis of thin-walled composite shells are studied. In the first analyze the sample without to consider geometric imperfections and then the effects of imperfections equal to the actual shell. The critical buckling dynamic is reported in load time that will show the sharp reduction in the buckling load with in increases load time and stiffens of shell is inversely to load time. This effect is more pronounced in the case of layup. With the increase of load time, the dynamic critical load dropped quickly and smaller than the critical buckling load is static. So in general, the choice of the static critical load is wrong as a criterion for dynamic design. In addition to the static buckling load, dynamic buckling load is reduced with increasing geometric imperfections of sample. Sensitivity to geometric imperfections is dependent on the type of the lay up. The geometric imperfections are the same effect on the dynamic critical load and static critical load for unlimited periods.