In civil, mechanical and aerospace engineering, structural stability is an important issue when concerning open, thin-walled elements; for example C, L or Z profiles. These components are commonly found in lightweight structures due to their high strength-to-weight ratio, and can be subjected to buckling phenomena regarding local, distortional and global stability. This thesis focuses on the global buckling of open thin-walled beams, with the main objective of implementing a Matlab code with an effective and versatile one-dimensional finite element formulation of literature. The Thesis combines theoretical formulations together with analytical and numerical modelling. Firstly, the general concepts of structural stability and elastic buckling are recalled, discussing different types of bifurcation.