Based on the mathematical model of the bending of the incompressible saturated poroelastic beam with axialdiffusion, the quasi-static bendings of the simply supported poroelastic beam subjected to a suddenly applied constant loadwere investigated, and the analytical solutions were obtained for different diffusion conditions of the pore fluid at the beamends. The deflections, the bending moments of the solid skeleton and the equivalent couples of the pore pressures werepresented in figures. It is also shown that the behavior of the saturated poroelastic beams depends closely on the diffusionconditions at the beam ends, especially for the equivalent couples of the pore pressures. It is found that the Mandel-Cryereffect also exists in the bending of the saturated poroelastic beams under specific diffusion conditions at the beam ends.