The subject of study was a thin-walled C-section made of carbon fiber reinforced polymer (CFRP). Column was subjected to eccentric compression in the established direction. In the computer simulation, the boundary conditions were assumed in the form of articulated support of the sections of the column. Particular studies included an analysis of the effects of eccentricity on the critical force value. The research was conducted using two independent research methods: numerical and experimental. Numerical simulations were done using the finite element method using the advanced system Abaqus®. The high sensitivity of the critical force value corresponding to the local buckling of the channel section to the load eccentricity was demonstrated.