This paper presents a new analytical solution for the vibration response of plates stiffened by orthogonal beams using a double finite sine integral transform technique. The compatibility conditions at the coupling interfaces and the boundary conditions of the plate are automatically defined in the transform. It is shown that the analytical model can accommodate various combinations of clamped and simply supported boundary conditions. The analytical model is then used to study the reproduction of the vibration response of an orthotropic plate. It is shown that an orthogonally ribbed isotropic plate can produce a closely matching vibration response to that of an orthotropic plate by carefully choosing an appropriate number of ribs and the rib properties in each plate direction.