Purpose <p>The effect of damping on the vibration behaviors of the structures is one of the most important problems in structural engineering. This study aims to establish a novel viscoelastic foundation model that consists of four parameters including two elastic parameters and two viscous coefficients. The proposed model is then employed to investigate the impacts of viscosity and porosity on the damped vibration characteristics of the functionally graded beams on viscoelastic foundations. The effect of the porosity is also considered in this study with several distribution models. </p> Methods <p>Higher-order shear deformation theory and Hamilton’s principle are used to derive the governing equations of motion. These equations are solved using the closed-form Navier solution. To validate the accuracy and proficiency of the current formulas and the calculation program, a few comparison studies are conducted. To demonstrate how certain parameters affect the damped vibration response of functionally graded porous beams, parametric research is conducted.</p> Results and Conclusions <p>The study’s findings demonstrated that the damped vibration characteristics of the functionally graded beams are significantly impacted by porosity and viscosity. Higher damping coefficients increase energy dissipation, resulting in a lower damped frequency of the functionally graded porous beams. The findings show that the two damping coefficients have opposing effects on various vibration modes: the first damping coefficient <i>c</i>_<i>d</i> primarily affects lower-frequency modes, whereas the second damping coefficient <i>c</i>_<i>s</i> is more important at higher frequencies. These revelations give important direction for the design and study of sophisticated structural systems by shedding light on vibration control techniques in porous FG structures supported by viscoelastic fluids.</p>