<p>In this paper, a general visco-Winkler–Pasternak foundation model is established to examine the vibration of functionally graded sandwich porous plates with various boundary conditions. The proposed viscoelastic foundation model introduces a new damping coefficient to account for the viscous effects in the shear layer, giving a more inclusive understanding of the vibrational behavior of the plates. The new viscoelastic foundation model can be easily reduced to other well-known foundation models by adjusting its parameters. The governing equations of motion are derived using a simple higher-order shear deformation theory and Hamilton’s principle. An analytical solution is applied to solve these equations under various boundary conditions, demonstrating the adaptability of the model. The accuracy and reliability of the proposed foundation model are validated through several comparative studies. A comprehensive parametric analysis is conducted to demonstrate the effects of some key parameters on the damped vibrational behavior of the sandwich plates. The results provide new insights into the damped vibration characteristics of functionally graded sandwich porous plates, highlighting the significant impact of the damping coefficients and porosity, as well as the boundary conditions of the plates. As obtained from the numerical results, the damped frequency decreases rapidly when the damping coefficients increase.</p>