In this study, the stability problem of a circular orthotropic cylindrical shell under the effect of an axial. compression varying with a power function of time is considered. At first, the modified Donnell type dynamic stability and compatibility equations are obtained using Love's shell theory. Applying the Galerkin method and Rayleigh-Ritz variational techniques to these equations and taking the large values of loading parameters into consideration, analytics are obtained for critical parameter values. The results show that critical parameters are affected by loading parameters variations, ratio of the Young's moduli variations, radius to thickness variations and the power of time in the axial compression expression variations. Comparing results with those in the literature validates the present analysis.