The aim of this study is to check how the change fiber configuration and geometric parameters affect the stability of a thin-walled angle column under compression. Buckling analysis of thin-walled structures made of bio-laminates was presented. Short angles with different configurations of reinforcing fibers and geometric parameters were studied. The laminate under analysis had a matrix made of epoxy resin reinforced with unidirectional flax fibers. The axially compressed structures were simply supported on both ends. Detailed numerical analyses were conducted by the finite element method using Abaqus software. The lowest two bifurcation loads and their corresponding eigenmodes were determined. Several configurations of unidirectional fiber arrangement with different width and length were tested. Results showed that the bio-laminate fiber configuration had a significant effect on the behavior of the compressed structure. Moreover, the change of geometrical parameters significantly influences the stability of the structure. In general, it was found that the bifurcation load decreased with the increase of the length of the L-profile column. However, increasing the flange width of the column resulted in a reduction of the bifurcation load (applies to a column with a length of 300 mm and longer). In paper the first stage of research is presented, which will be experimentally verified in subsequent studies.