This paper presents a continuum mechanics approach to analyze the viscoelastic acoustic response of two-layer polymer films deposited on solid surfaces in a fluid environment. The study derives the general solution of a wave equation describing the dynamics of such viscoelastic materials and calculates the acoustic response to applied shear stress. The results show that the shift in quartz crystal resonance frequency and dissipation factor strongly depend on the viscous loading of the adsorbed layers and the shear storage and loss moduli of the overlayers. These findings are applicable to quartz crystal acoustical measurements of viscoelastic polymers and layered structures like protein films. The analysis considers two viscoelastic layers covering a quartz plate oscillating in a bulk liquid. The viscoelastic material is modeled as a Voigt element, with its parallel arrangement of a spring and a dashpot. The study shows that even very thin viscoelastic films can dissipate significant energy when the quartz plate oscillates in a liquid. The results demonstrate that the resonance frequency shift and dissipation factor depend on the viscoelastic properties of the layers and the surrounding medium. The paper also discusses the "no-slip" boundary conditions at the solid-overlayer interface and derives the general solution for the wave equation with these conditions. The results are analyzed in the limit cases of thin and thick viscoelastic layers. For thin layers, the Sauerbrey relation is recovered, while for thick layers, the results depend on the viscoelastic properties of the layers. The study shows that the viscous bulk loading of the overlayer allows for the measurement of its viscoelastic properties using simultaneous measurements of the resonance frequency shift and dissipation factor in a liquid environment. The results are applicable to the measurement of viscoelastic properties of adsorbed proteins and polymer films in a liquid environment. The paper also presents numerical simulations of the acoustic response of thin viscoelastic layers and shows that the viscoelastic properties of the layers significantly affect the resonance frequency and dissipation factor. The study provides a framework for understanding the viscoelastic behavior of layered structures in fluid environments and has potential applications in biosensing and material science.This paper presents a continuum mechanics approach to analyze the viscoelastic acoustic response of two-layer polymer films deposited on solid surfaces in a fluid environment. The study derives the general solution of a wave equation describing the dynamics of such viscoelastic materials and calculates the acoustic response to applied shear stress. The results show that the shift in quartz crystal resonance frequency and dissipation factor strongly depend on the viscous loading of the adsorbed layers and the shear storage and loss moduli of the overlayers. These findings are applicable to quartz crystal acoustical measurements of viscoelastic polymers and layered structures like protein films. The analysis considers two viscoelastic layers covering a quartz plate oscillating in a bulk liquid. The viscoelastic material is modeled as a Voigt element, with its parallel arrangement of a spring and a dashpot. The study shows that even very thin viscoelastic films can dissipate significant energy when the quartz plate oscillates in a liquid. The results demonstrate that the resonance frequency shift and dissipation factor depend on the viscoelastic properties of the layers and the surrounding medium. The paper also discusses the "no-slip" boundary conditions at the solid-overlayer interface and derives the general solution for the wave equation with these conditions. The results are analyzed in the limit cases of thin and thick viscoelastic layers. For thin layers, the Sauerbrey relation is recovered, while for thick layers, the results depend on the viscoelastic properties of the layers. The study shows that the viscous bulk loading of the overlayer allows for the measurement of its viscoelastic properties using simultaneous measurements of the resonance frequency shift and dissipation factor in a liquid environment. The results are applicable to the measurement of viscoelastic properties of adsorbed proteins and polymer films in a liquid environment. The paper also presents numerical simulations of the acoustic response of thin viscoelastic layers and shows that the viscoelastic properties of the layers significantly affect the resonance frequency and dissipation factor. The study provides a framework for understanding the viscoelastic behavior of layered structures in fluid environments and has potential applications in biosensing and material science.