Thin-walled elements, thanks to their good properties, are increasingly used in structural applications, especially in the aircraft and building industries. These kinds of structures are often perforated for reducing weight and to ease servicing and maintenance operations, e.g., in aircraft wing ribs. These perforations cause a redistribution of stresses in the element which may change the ultimate strength of the structure and their elastic stiffness. The buckling behaviour of structural members with perforations is significantly influenced by the size, location, shape and number of perforations. Therefore, it is necessary to investigate the influence of these kinds of cut-out parameters on thin-walled structure buckling and postbuckling behaviour. This study investigated numerically the buckling and postbuckling behaviour of thin-walled perforated composite profiles with a Z-cross-section subjected to compression load. Numerical calculations were performed using the finite element method in the ABAQUS® program. The study investigated the effect of localisation and geometric parameters of cut-outs on the buckling load, postbuckling equilibrium path and failure load. Moreover, the perforated profiles were compared with a profile without cut-outs, which were experimentally tested in previous research. Results showed that the perforated profiles with a Z-cross-section do not lose their stability in the post-critical range. What is more, a well-chosen arrangement of the holes may prevent the mechanical properties from deteriorating.