The current demand for lightweight structures in a wide range of engineering applications leads to using thin-walled composite laminated structures whose behaviour is governed by buckling and postbuckling phenomena. Such a demand is pushing the borders of computational mechanics to enhance methods and algorithms for studying those structures’ geometrically nonlinear responses. In light of these premises, this work presents some of the authors' developments in analysing lightweight composite laminated structures. The first part introduces a family of finite elements known as MISS elements [1], where MISS stands for mixed isostatic self-stress equilibrated. In particular, two quadrilateral shell elements with four and eight nodes [2], respectively and one hexahedral solid-shell element are presented. The description of those elements, which are derived from the Hellinger-Reissner functional, is followed by a discussion on their advantages concerning displacement-based elements when studying composite laminated thin-walled structures. Subsequently, a framework for the postbuckling analysis of composite structures with MISS elements that uses either the Koiter multi-modal approach [3] or a path-following analysis with the Riks’ algorithm is presented. The robustness and efficiency of that framework are shown through numerical results, which span from the fast imperfection sensitivity analysis of composite laminated structures governed by strong modal interaction phenomena to the optimisation of thin walled structures subjected to compressive stresses. REFERENCES [1] A. Madeo, G. Zagari, R. Casciaro, S. de Miranda, A mixed 4-node 3D plate lement based on self-equilibrated isostatic stresses, Interational Journal of Structural Stability and Dynamics, 15, 1450066, 2015. [2] A. Madeo, FS Liguori, G. Zucco, S. Fiore, International Journal for Numerical Methods in Engineering, 122(1), 82-121, 2021. [3] A. Madeo, RMJ Groh, G Zucco, PM Weaver, G. Zagari, R. Zinno, Post-buckling analysis of variable angle tow composite plates using Koiter’s approach and the finite element method, Thin-Walled Structures, 110, 1-13, 2017.