Abstract: The results of the numerical studies of the influence of the reinforcement orientation of rigid layers and relative thickness of a soft isotropic viscoelastic polymer layer on the values of natural frequencies and loss factors of the coupled vibrations of symmetric and asymmetric unsupported three-layer rectangular composite plates are discussed. It is shown that in a symmetric three-layer plate, a flexural and torsion interaction arises generating mutual transformations of the natural forms of the coupled vibration modes if at least one of its natural forms in the plate directions is characterized by an even number of quarter-wavelengths, and another natural form is characterized by an odd number of quarter-wavelengths. A flexural–flexural interaction arises in an asymmetric unsupported three-layer plate and generates mutual transformations of the natural forms of coupled vibration modes in two mutually orthogonal planes if both natural forms are characterized by either an even or an odd number of quarter-wavelengths in the main directions of the plate. It has been found that each mode of the natural vibrations of the three-layer plates corresponds to the effective relative thickness of the soft isotropic viscoelastic polymer layer.