In accordance with the method described in /1–3/, a derivation of two-dimensional equations of motion is given for a thin two-layer (non-symmetric) elastic plate. The mean values of the bending stiffness, the density, and Poisson's ratio are found, and the position of the middle plane is determined. In the coordinate system attached to this plane, the system of equations is separated into quasistatic equations for the longitudinal motion and a dynamic equation (of the ordinary kind) for the transverse component of the displacement. Unlike /1–3/, only one characteristic dimension in the longitudinal direction is introduced, which turns out to be sufficient and simplifies the analysis. Formulae of the complete field of stresses are provided. Stresses, which are of secondary importance for homogeneous plates, may be essential when the strength of the joint of the layers is considered.