Porous materials with microscopic structures like foam, sponges, lung tissues and lung substitute materials have particular characteristics, which differ from those of solid materials. Ion beams passing through porous materials show much stronger energy straggling than expected for non-porous solid materials of the same thickness. This effect depends on the microscopic fine structure, the density and the thickness of the porous material. The beam-modulating effect from a porous plate enlarges the Bragg peak, yielding similar benefits in irradiation time reduction as a ripple filter. A porous plate can additionally function as a range shifter, which since a higher energy can be selected for the same penetration depth in the body reduces the scattering at the beam line and therefore improves the lateral fall-off. Bragg curve measurements of ion beams passing through different porous materials have been performed in order to determine the beam modulation effect of each. A mathematical model describing the correlation between the mean material density, the porous pore structure size and the strength of the modulation has been developed and a new material parameter called 'modulation power' is defined as the square of the Gaussian sigma divided by the mean water-equivalent thickness of the porous absorber. Monte Carlo simulations have been performed in order to validate the model and to investigate the Bragg peak enlargement, the scattering effects of porosity and the lateral beam width at the end of the beam range. The porosity is found to only influence the lateral scattering in a negligible way. As an example of a practical application, it is found that a 20 mm and 50 mm plate of Gammex LN300 performs similar to a 3 mm and 6 mm ripple filter, respectively, and at the same time can improve the sharpness of the lateral beam due to its multifunctionality as a ripple filter and a range shifter.