Abstract: Based on a three-parameter Winkler-Pasternak viscoelastic foundation model, the free vibration behavior of porous functionally graded viscoelastic material (FGVM) beams in thermal environment subjected to initial axial mechanical force is investigated. Temperature distribution is determined by a one-dimensional steady-state heat conduction equation. The material properties are temperature-dependent and described by using Kelvin-Voigt model according to the modified mixture power-law distribution form with even porosity for FGVM beams. Based on n-th order generalized beam theory, the dynamic governing equations for this system are derived by using Hamiltonian principle. An generalized form for Navier method can be utilized to obtain the exact coupling vibration responses of the FGVM beams with both clamped ends, clamped at one end and hinged at the other end, and hinged at both ends. The effects of different beam theories, boundary conditions, thermal-mechanical loads, viscoelastic foundation parameters, structural damping coefficient, porosity, material graded index, length-to-thickness ratio and mode number on the dynamic behavior of FGVM beams are discussed by several numerical examples.