Two practical methods are proposed to measure the tortuosity of a porous or permeable material from its tomographic reconstruction. The first method is based oil the direct measurement of the shot-test distance between two points in the pores, and the second is based on the geodesic reconstruction of the pore or permeation space. Unlike the first method, the second can be directly applied to gray-tone tomograms, without the need of a segmentation step. The methods are illustrated with an electron tomogram of clay/plastic nanocomposite, an X-ray microtomogram of sandstone, and a series of model morphologies consisting of penetrable random spheres. For the latter series, the measured tortuosities compare very well with those derived independently front the theoretical effective diffusion coefficients. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 2000-2012, 2009