The multi-layered plate vibration is investigated. A two-dimensional asymptotic model of the second order accuracy with respect to the small thickness parameter is proposed with account for the transverse shear and the normal fibre extension. The model is appropriate for a monoclinic plate described by 13 elastic moduli which is heterogeneous in the thickness direction. In particular, the model can be applied to a multi-layered plate consisting of orthotropic layers of arbitrary orientation. In this case the elastic moduli are piece-wise constant functions.
