This paper presented a three dimensional analysis for the buckling behavior of an imperfect orthotropic thick cylindrical shells under pure axial or external pressure loading. Critical loads are computed for different imperfection parameter. Both ends of the shell have simply supported conditions. Governing differential equations are driven based on the second Piola–Kirchhoff stress tensor and are reduced to a homogenous linear system of equations using differential quadrature method. Buckling loads reduction factor is computed for different imperfection parameters and geometrical properties of orthotropic shells. The sensitivity is established through tables of buckling load reduction factors versus imperfection amplitude. It is shown that imperfections have higher effects on the buckling load of thin shells than thick ones. Results show that the presented method is very accurate and can capture the various geometrical imperfections observed during the manufacturing process or transportation.
 Lundquist, E. E. Strength Tests of Thin-Walled Duralumin Cylinders in Compression. NACA Report No. 473, June 1933.
 Donnell, L. H. A New Theory for the Buckling of Thin Cylinders Under Axial Compression and Bending. Transactions of the American Society of Mechanical Engineers, 56 (1934), 795-806.
 Wilson, W. M., N. M. Newmark. The Strength of Thin Cylindrical Shells and Columns. University of Illinois Engineering Experiment Station, Bulletin 255, Feb. 1933.
 Kepple, J., B. G. Prusty, G. Pearce, D. Kelly, R. Thomson, R. Degenhardt. Influence of Imperfections on Axial Buckling Load of Composite Cylindrical Shells. The 19th International Conference on Composite Materials. 2012.
 Koiter, W. T. On the Stability of Elastic Equilibrium. NASA TT-F-10833, National Aeronautics and Space Administration, USA, 1967.
 Degenhardt, R., A. Kling, A. Bethge, J. Orf, L. Kärger, K. Rohwer, et al. Investigations of Imperfection Sensitivity of Unstiffened CFRP Cylindrical Shells. Composite Structures, 92 (2010), 1939-1946.
 Lee, M. C. W., R. M. Payne, D. W. Kelly, R. S. Thomson. Determination of Robustness for a Stiffened Composite Structure Using Stochastic Analysis. Composite Structures, 86 (2008), 78-84.
 Orifici, A. C., R. S. Thomson, R. Degenhardt, C. Bisagni, J. Bayandor. A Finite Element Analysis Methodology for Analyzing Degradation and Collapse in Postbuckling Composite Aerospace Structures. Journal of Composite Materials, 43 (2009), 3239-3263.
 Orifici, A. C., R. S. Thomson, R. Degenhardt, C. Bisagni, J. Bayandor. An Analysis Tool for Design and Certification of Postbuckling Composite Aerospace Structures. International Journal of Structural Stability and Dynamics, 10 (2010), 669-681.
 Hühne, C., R. Rolfes, E. Breitbach, J. Tessmer. Robust Design of Composite Cylindrical Shells Under Axial Compression - Simulation and Validation. Thin-Walled Structures, 46 (2008), 947-962.
 Skukis, E., O. Ozolins, K. Kalninsa, M. A. Arbelob. Experimental Test for Estimation of Buckling Load on Unstiffened Cylindrical Shells by Vibration Correlation Technique. Procedia Engineering, 172 (2017), 1023-1030.
 Alashti, R. A., S. A. Ahmadi. Buckling of Imperfect Thick Cylindrical Shells and Curved Panels with Different Boundary Conditions Under External Pressure. Journal of Theoretical and Applied Mechanics, 52 (2014) no. 1, 25-36.
 Semenyuk, N. P., N. B. Zhukova. Stability and Post-buckling Behavior of Orthotropic Cylindrical Shells with Local Deflections, International Applied Mechanics, 52 (2016) No. 3, 290-300.
 Winterstetter, T. A., H. Schmidt. Stability of Circular Cylindrical Steel Shells Under Combined Loading. Thin-Walled Structures, 40 (2002), 893-909.
 Lai, W. M., D. Rubin, E. Krempl. Introduction to Continuum Mechanics. 3rd ed. Butterworth-Heinemann, Massachusetts, 1996.
 Bellman, R. E., J. Casti. Differential quadrature and long term Integration. Journal of Mathematical Analysis and Applications, 34 No. 1 (1971), 235-238.
 Shu, C. Differential Quadrature and Its Application in Engineering. Springer-Verlag, London, UK, 2000.
 Kardomateas, G. A. Benchmark Three-Dimensional Elasticity Solution for the Buckling of Thick Orthotropic Cylindrical Shells. Journal Applied Mechanics, (ASME).5 (1996), 569.
 Timoshenko, S. P., J. M. Gere. Theory of Elastic Stability. McGraw-Hili Co., New York, 1961.