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Abstract We derive the oblateness parameter q of the dark matter halo of a sample of gas-rich, face-on disk galaxies. We have assumed that the halos are triaxial in shape but their axes in the disk plane ( a and b ) are equal, so that q = c / a measures the halo flattening. We have used the H i velocity dispersion, derived from the stacked H i emission lines and the disk surface density, determined from the H i flux distribution, to determine the disk potential and the halo shape at the R 25 and 1.5 R 25 radii. We have applied our model to 20 nearby galaxies, of which six are large disk galaxies with M (stellar) > 10 10 , eight have moderate stellar masses, and six are low-surface-brightness dwarf galaxies. Our most important result is that gas-rich galaxies that have M (gas)/ M (baryons) > 0.5 have oblate halos ( q < 0.55), whereas stellar-dominated galaxies have a range of q values from 0.21 ± 0.07 in NGC4190 to 1.27 ± 0.61 in NGC5194. Our results also suggest a positive correlation between the stellar mass and the halo oblateness q , which indicates that galaxies with massive stellar disks have a higher probability of having halos that are spherical or slightly prolate, whereas low-mass galaxies have oblate halos ( q < 0.55).