The paper presents a comprehensive analysis of the viscoelastic acoustic response of layered polymer films at fluid-solid interfaces, using a continuum mechanics approach. The authors derive the general solution to the wave equation describing the dynamics of two-layer viscoelastic polymer materials deposited on a solid (quartz) surface in a fluid environment. They focus on the acoustic response of the system to applied shear stress, specifically the shift in the quartz generator resonance frequency and the dissipation factor, which strongly depend on the viscous loading of the adsorbed layers and the shear storage and loss moduli of the overlayers. The study uses the Voight model of viscoelastic elements, where the complex shear modulus is described by a real part (storage modulus) independent of frequency and an imaginary part (loss modulus) that increases linearly with frequency. The authors analyze both "thin" and "thick" layer acoustic responses, showing that even thin viscoelastic layers can dissipate significant energy when the quartz plate oscillates in a liquid phase. They derive expressions for the resonance frequency shift and the dissipation factor, which can be used to determine the viscoelastic properties of the overlayer from QCM measurements. The results are applicable to quartz crystal acoustic measurements of viscoelastic polymers and biomolecular films, such as protein layers adsorbed from solution onto self-assembled monolayers. The study highlights the importance of considering the viscoelastic behavior of adsorbed layers in the context of biomolecular sandwich structures, which have potential applications in molecular biosensors and medical and environmental fields.The paper presents a comprehensive analysis of the viscoelastic acoustic response of layered polymer films at fluid-solid interfaces, using a continuum mechanics approach. The authors derive the general solution to the wave equation describing the dynamics of two-layer viscoelastic polymer materials deposited on a solid (quartz) surface in a fluid environment. They focus on the acoustic response of the system to applied shear stress, specifically the shift in the quartz generator resonance frequency and the dissipation factor, which strongly depend on the viscous loading of the adsorbed layers and the shear storage and loss moduli of the overlayers. The study uses the Voight model of viscoelastic elements, where the complex shear modulus is described by a real part (storage modulus) independent of frequency and an imaginary part (loss modulus) that increases linearly with frequency. The authors analyze both "thin" and "thick" layer acoustic responses, showing that even thin viscoelastic layers can dissipate significant energy when the quartz plate oscillates in a liquid phase. They derive expressions for the resonance frequency shift and the dissipation factor, which can be used to determine the viscoelastic properties of the overlayer from QCM measurements. The results are applicable to quartz crystal acoustic measurements of viscoelastic polymers and biomolecular films, such as protein layers adsorbed from solution onto self-assembled monolayers. The study highlights the importance of considering the viscoelastic behavior of adsorbed layers in the context of biomolecular sandwich structures, which have potential applications in molecular biosensors and medical and environmental fields.