Applying Fourier series in a direction to a thin elastic plate, we may obtain basic ordinary differential equations for a static problem. When the equations are solved analytically, we can obtain not only solutions of static boundary-value problems but also a shape function of the plate that satisfies the basic equations. Introducing orthotropic material properties into the plate, we get the stiffness matrix and the shape function corresponding to the matrix. Adopting the shape function, we construct the consistent mass matrix of the plate. Applying the stiffness and the mass matrices to various folded plate structures composed of the plates, we demonstrate the characteristic feature of the procedure.