This study investigates the effect of eccentric compressive load on the stability, critical states and load-carrying capacity of thin-walled composite Z-profiles. Short thin-walled columns made of carbon fiber-reinforced plastic composite material fabricated by the autoclave technique are examined. In experimental tests, the thin-walled structures were compressed until a loss of their load-carrying capacity was obtained. The test parameters were measured to describe the structure’s behavior, including the phenomenon of composite material failure. The post-critical load-displacement equilibrium paths and the acoustic emission signal enabling analysis of the composite material condition during the loading process were measured. The scope of the study also included performing numerical simulations by finite element method to solve the problem of non-linear stability and to describe the phenomenon of composite material damage based on the progressive failure model. The obtained numerical results showed a good agreement with the experimental characteristics of real structures. The numerical results are compared with the experimental findings to validate the developed numerical model.