In this paper, a meshfree Galerkin method that is based on the first-order shear deformation theory (FSDT) will be introduced to analyse the elastic bending problem of stiffened and un-stiffened folded plates under different loadings and boundary conditions. Folded plates are regarded as assemblies of plates that lie in different planes. The stiffness matrices of the plates are given by the meshfree method. Employing the element concept, which is borrowed from the finite element method, and treating every plate as a big element, the global stiffness matrix of the whole folded plate is obtained by superposing the stiffness matrices of the plates. This is about the same for the analysis of stiffened folded plates. They are considered as assemblies of stiffened plates. The stiffness matrices of the stiffened plates are also given by the meshfree method. Superior to the finite element methods, no mesh is required in determining the stiffness matrices for the plates and the stiffened plates in this paper, which means time-consuming and accuracy-suffering remeshing is entirely avoided for problems such as large deformation or crack propagation in folded plates or stiffener position changes of stiffened folded plates. To demonstrate the accuracy and convergence of the method, several numerical examples are calculated by it and the finite element commercial software ANSYS. Good agreement is observed between the two sets of results. © 2006 Elsevier Ltd. All rights reserved.