Abstract: The stability and vibration behavior of functionally graded material (FGM) beams resting on a Winkler-Pasternak elastic foundation under the action of initial axial mechanical load considering the hygro-thermal environment is investigated. Three hygro-thermal distributions through the thickness of the beams are assumed. The material properties are temperature-dependent and are distributed according to the Voigt mixture power law model. An n-th order generalized beam theory is proposed. The governing equations of buckling and free vibration are derived from the Hamilton's principle, in which the fundamental unknown functions are the axial displacement, bending and shear components of the transverse displacement. Applying the Navier method, the analytical solutions of the buckling and free vibration responses of FGM simply supported beams are obtained. The availability and accuracy of the n-th order generalized beam theory are tested and discussed through several numerical examples. The results show that it refines the beam theories and can be used as a benchmark to verify or modify other shear deformation beam theories. The effects of three types of hygro-thermal distribution, moisture and temperature rise, initial axial mechanical load, length-to-thickness ratio, elastic foundation stiffness and material graded index on the stability and vibration behavior of FGM beams are analyzed.