This paper reports the results of a numerical analysis of buckling in a carbon-fibre reinforced plastic (CFRP). The analysis involved determination of the first buckling mode and critical forces for the tested composite. The composite was tested for six different ply orientations. The analysis was performed on a closed section composite column. The objective of the analysis was to determine critical forces affecting the composite profiles with the applied ply orientations and, thus, to determine the laminate ply orientations which can carry the heaviest loads. The numerical modelling and all computations were performed using the Abaqus 6.14 software. In the analysis, we took account of boundary conditions and performed a discretization process in order to obtain correct results.