The analysis of slender structures, characterized by complex buckling and postbuckling phenomena and by a strong imperfection sensitivity, is heavily penalized by the lack of adequate computational tools. Standard incremental iterative approaches are computationally expensive and unaffordable, while FEM implementation of the Koiter method is a convenient alternative. The analysis is very fast, its computational burden is of the same order as a linearized buckling load evaluation and the simulation of different imperfections costs only a fraction of that needed to characterize the perfect structure. The main objective of the present work is to show that finite element implementations of the Koiter method can be both accurate and reliable and to highlight the aspects that require further investigation.