Object and purpose of research. The study is concerned with a three-layer plate formed by two rigid anisotropic layers and a soft medium isotropic layer of viscoelastic polymer. Each rigid layer presents anisotropic structure formed by a finite number of randomly oriented orthotropic viscoelastic layers of composites.The paper is intended to study the influence of reinforcement orientation of rigid layers, relative thickness of the soft layer of an isotropic viscoelastic polymer and the ambient temperature on values values of natural frequencies and mechanical loss factors of the coupled damped oscillations in symmetric and assymetric plates.Materials and methods. Numerical experiment using a computer program implementing the previously proposed method for solving coupled differential equations of damped oscillations in anisotropic three-layer plates [2].Main results. It was shown that in unsupported globally monoclinic symmetrical three-layer rectangular plate a bending-torsional interaction occurs, generating mutual transformations of the eigenforms of the coupled oscillation modes if at least in one of the directions of the plate one of the eigenforms is characterized by an even number of quarters of the wave, and theother eigenform is characterized by an odd number of quarters of the wave. In unsupported globally orthotropic asymmetric three-layer rectangular plate interaction of bending modes of oscillations occurs in two mutually orthogonal planes, if botheigenforms are characterized by either an even or an odd number of wave quarters in main directions of the plate.It was found that each mode of natural oscillations of both symmetric and asymmetric three-layer plates has its own effective relative thickness of the soft layer of an isotropic viscoelastic polymer corresponding to the maximum level of dissipative prop-erties. A further increase in the relative thickness is often accompanied by a decrease in values of the mechanical loss factors.The significant influence of ambient temperature on natural frequencies values and mechanical loss factors of all considered oscillation modes of symmetric and asymmetric unsupported rectangular three-layer composite plates is demonstrated. Conclusion. It was found that coupled damped oscillations of a symmetric three-layer plate are described by two systems of differential equations, with structures close to that of the systems of corresponding differential equations describing the damped oscillations of a quasi-homogeneous monoclinic plate. At the same time, the coupled damped oscillations of an asymmetric three-layer plate are described by two systems of differential equations that coincide with the systems of corresponding differ- rential equations describing the damped oscillations of a globally orthotropic three-layer plate.