We analyze a behavior of viscoelastic composite structures. We present a method of generalized complex forms, which, contrary to the well-known methods, allows us to take into account variation of viscoelastic properties with the frequency of vibration and heterogeneous character of stress distribution in structures. The method does not impose limitations on the number of functions, which describe the material viscoelastic properties. The advantages of the method presented here are demonstrated by solution of the problem of forced oscillations of a three-layered ring loaded by external impact and subjected to harmonic oscillations. The influence of viscoelastic Poisson’s ratio on the amplitude of forced oscillations of viscoelastic structures is studied.