This paper aims to examine flexural vibrations of fully saturated poroelastic structures on an elastic bed subjected to moving point loads via an analytical solution. Using a flexural beam model in conjunction with the Biot's poro-elasticity theory, the equations of motion of the porous structure are derived. Using assumed mode method and Laplace transform, the explicit expressions of displacement and pore pressure are obtained carefully.For a particular case, the predicted results are also compared with those of another work and a reasonably good agreement is achieved. The influences of the moving load velocity, permeability ratio, transverse stiffness of the foundation, viscosity of the pore fluid, and porosity on the maximum elasto-dynamic fields and pore pressure are conclusively discussed.The velocity pertinent to the maximum possible dynamic response is graphically determined and the roles of influential parameters on this crucial factor are displayed. The present model could be easily extended to multi-layered poroelastic structures under moving loads.