In this paper, axial buckling of a composite cylindrical shell with and without a rectangular cutout is studied based on the first-order shear deformation theory. The equations are derived in a general form and can be converted to Donnell`s, Love`s, and Sanders` theories. To investigate the perforated shell, a physical domain is decomposed into several elements with uniform boundary and loading conditions in each element edges. In each element, the governing equations are discretized in both longitudinal and circumferential directions by the use of generalized differential quadrature method (GDQM). By assembling these discretized relations, a system of algebraic equations is generated. The boundary conditions at the shell and cutout edges, and the compatibility conditions at the interface boundaries of adjacent elements are also discretized by GDQM. Finally, the buckling load is calculated by an eigenvalue solution. To validate the presented method, the results of GDQM are compared with the available ones in the literature and also with ABAQUS finite element model. Then a parametric analysis is performed to investigate the effects of different parameters on the buckling behavior of the shells with and without cutouts. This study illustrates that the shell layup has a great effect on the buckling load of a shell. In addition, the influence of increasing the cutout size is not identical for different layups. However, the buckling behavior is independent of the shell material. Moreover, it was concluded that the shell with a square cutout has higher critical load than the one with a rectangular opening.