When a saturated porous material is deformed, pressure gradients are created in the Liquid, and the liquid flows within the pores to equilibrate the pressure. This phenomenon can be exploited to measure permeability: A rod of saturated porous material is instantaneously bent by a fixed amount, and the force required to sustain the deflection is measured as a function of time. The force decreases as the liquid flows through the pore network, and the rate of decrease depends on the permeability. This technique has been applied successfully to determine the permeability of gels, as well as their viscoelastic properties; in this paper the method is extended to ceramic materials, such as porous glass and cement paste. The theory has been modified to take account of the compressibility of the solid and liquid phases (whereas, those factors are negligible for gels), Analyses are presented for constant deflection, constant rate of deflection, and sinusoidal oscillation, where the solid phase is either purely elastic or viscoelastic, and the beam is either cylindrical or square. Experimental tests on Vycor(R) glass and cement paste will be presented in companion papers.