Summary Methane hydrate was formed in two moist sands and a sand/silt mixture under a confining stress in an X-ray-transparent pressure vessel. Three initial water saturations were used to form three different methane-hydrate saturations in each medium. X-ray computed tomography (CT) was used to observe location-specific density changes caused by hydrate formation and flowing water. Gas-permeability measurements in each test for the dry, moist, frozen, and hydrate-bearing states are presented. As expected, the effective permeabilities (intrinsic permeability of the medium multiplied by the relative permeability) of the moist sands decreased with increasing moisture content. In a series of tests on a single sample, the effective permeability typically decreased as the pore space became more filled in the order of dry, moist, frozen, and hydrate-bearing. In each test, water was flowed through the hydrate-bearing medium and we observed the location-specific changes in water saturation using CT scanning. We compared our data to a number of models, and our relative permeability data compare most favorably with models in which hydrate occupies the pore bodies rather than the pore throats. Inverse modeling (using the data collected from the tests) will be performed to extend the relative permeability measurements.