This paper presents a novel approach for accurate and efficient planar response analysis of
cellular beams, which provides the necessary input for local out-of-plane buckling analysis of web
components. The proposed approach utilises the super-element concept defined for unit-cells,
achieving further efficiencies through an enhanced Element-Free Galerkin (EFG) approach for
establishing the planar super-element response. Several examples are presented, firstly at the level of
unit-cells, where the computational benefits of the EFG method are highlighted, and finally at the
overall level of cellular beams, where the superior performance of the unit-cell approach with virtually
no compromise in accuracy is demonstrated.