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The subject of the research was a thin-walled plate weakened by a cut-out, made of carbon-epoxy laminate, subjected to compression. The study included an analysis of the critical and weakly post-critical behaviour using experimental and numerical methods. As a result of the research conducted on physical plates, a post-critical equilibrium paths, which were then used to determine the critical loads by approximation methods, were determined. Simultaneously, numerical calculations with finite element method were performed, using linear analysis of eigenvalue problems, which the results led to determination of the critical loads for the developed numerical model. The second step of the calculations included the performing of nonlinear analysis of the structure with initiated geometrically imperfection corresponding to the flexural–torsional buckling mode of the plate. The numerical results were compared with the experimental funding, revealing that the developed numerical model of the structure was correct. The numerical simulations were performed using the ABAQUS® software.