Abstract: By using finite differences in semi-discretization of the governing equations and boundary conditions, the equations are restricted on discrete mesh lines and then solved by the weighted residual method. This is the weighted residual method of lines proposed in this paper, which mayas well be called finite difference-weighted residual dimension-wise coupled method. Taking orthotropic thin plates as the working example, present paper gives the detailed formulation and the associated numerical examples to show the effectiveness of the proposed method.