A simple beam-bending measurement can be used to determine the permeability, as well as the modulus, of a saturated porous material. The procedure is to apply a constant deflection and measure the load decay as the pressure in the pores equilibrates; alternatively, an oscillatory deflection can be applied and the phase delay measured. The analysis of the experiment has been previously presented for beams with square or round cross sections. In this article, we consider the case of a saturated porous beam with a rectangular cross section and transverse isotropy; that is, the permeability and elastic properties are uniform in the x(1)-x(2) plane, but have different values in the x(3) direction. This is the case for a sedimentary stone or laminated composite, for example. The kinetics of hydrodynamic relaxation depend on the orientation of the planes with respect to the bending axis; consequently, three different solutions are presented that allow determination of the properties in etch direction. Exact solutions are obtained for elastic beams; in approximation for the case of a viscoelastic anisotropic beam also is presented. The relaxation kinetics of an isotropic rectangular plate are obtained as a special case; that geometry is convenient to use for isotropic materials, such as cement paste or mortar.