AbstractAn edge‐based smoothed finite element method using 3‐node triangular membrane elements (ES‐FEM‐T3) is proposed to analyze three‐dimensional (3D) spatial membrane structures under large deflection, rotation, and strain. In our 3D formulation, co‐rotational local coordinate systems associated with the edge‐based smoothing domains are constructed. Edge‐based gradient smoothing for the spatial membrane structure is performed in global Cartesian coordinate system and transformed into the co‐rotational local coordinate system. The smoothed strain and stress can then be properly evaluated in the co‐rotational local coordinate system after the elimination of the rigid body motions simply by coordinates transformation. Explicit time integration scheme is used to compute the transient response of the 3D spatial membrane structure to time‐domain excitations, and the dynamic relaxation method is employed to obtain steady‐state solutions. The numerical results demonstrate that the proposed method produces much better solution accuracy and computational efficiency than the standard FEM using T3 membrane element. Copyright © 2010 John Wiley & Sons, Ltd.