This dissertation addresses the issue of non-linear stability of frame structures consisting of thin-walled composite beam elements. To this end, a numerical approach is presented that involves the development of an original 1D finite element model. The research delves into several key aspects. Firstly, the dissertation introduces the research problem and scientific motivation and outlines the main objectives and purpose of the study. A brief overview of previous studies on buckling of thin-walled composite beams is also provided. The study delves into composite materials, with a particular emphasis on fiber-reinforced composites. It explores the macromechanics of single-layer composites, specifically those with arbitrarily oriented layers under plane stress and deformation conditions. The research also focuses on the fundamentals of mechanics for thin-walled composite beam supports, considering the influence of shear deformations. The underlying assumptions of the proposed model are discussed, and the displacement field of the thin-walled cross-section is defined, considering both linear and nonlinear components. The internal forces of the crosssection are analyzed, particularly for cross-ply and angle laminated cross-sections. The dissertation also describes the procedure for calculating the cross-section properties. In addition, a computer program CCSC for the calculation of composite cross-section properties has been developed. A finite element formulation is presented to analyze the stability of the frame structures. The model is designed to perform both linearized and nonlinear stability analysis. The finite element of the beam consists of 14 degrees of freedom and employs the principle of virtual work to derive the elastic and geometric stiffness matrices. The nonlinear analysis is performed using an incremental iterative method based on the generalized displacement control method. The updated Lagrangian formulation is utilized to solve the equilibrium equations. The dissertation includes the development of the THINWALL V18 computer program, and a large number of examples are analyzed to validate the numerical model, considering different cross-sections of symmetric and balanced composites, as well as various boundary conditions and different frame structures. The study concludes with a discussion of the contributions and scientific achievements. It also identifies possible directions for future research and suggests improvements in the field of buckling of thin-walled composite beams, particularly with regard to the inclusion of shear deformations. Overall, this dissertation provides a comprehensive numerical approach to evaluate the nonlinear stability of frame structures composed of thin-walled composite beam elements. By enhancing the understanding and optimization of such structures, this research contributes to the advancement of structural engineering in the field of composite materials.