The free and forced vibrations of a system of two rectangular membranes attached together by a Winkler elastic layer are studied analytically. The motion of the system is described by two non-homogeneous partial differential equations. The solutions of the free vibrations are obtained by the Bernoulli-Fourier method. Solving the boundary value problem the natural frequencies and the mode shape functions are found. The initial-value problem is also solved. The free vibrations of the double-membrane system are realised by synchronous and asynchronous deflections. The forced vibrations of membranes subjected to arbitrarily distributed continuous loads are determined by using the classical method of the expansion in a series of the normal modes of vibrations. Discussing the vibrations caused by the harmonic exciting forces it is shown that the dynamic absorption phenomenon appears. Therefore, the double-membrane system can be used as a dynamic vibration absorber. As a numerical example the vibrations of the system consisting of two identical membranes subjected to harmonic uniform distributed load are treated in detail.