Abstract We determine radial velocities and mass flow rates in a sample of 54 local spiral galaxies by modeling high-resolution and high-sensitivity data of the atomic hydrogen emission line. We found that, although radial inflow motions seem to be slightly preferred over outflow motions, their magnitude is generally small. Most galaxies show radial flows of only a few km s−1 throughout their H i disks, either inward or outward, without any clear increase in magnitude in the outermost regions, as we would expect for continuous radial accretion. Gas mass flow rates for most galaxies are less than 1 M ⊙ yr−1. Over the entire sample, we estimated an average inflow rate of 0.3 M ⊙ yr−1 outside the optical disk and of 0.1 M ⊙ yr−1 in the outskirts of the H i disks. These inflow rates are about 5–10 times smaller than the average star formation rate of 1.4 M ⊙ yr−1. Our study suggests that there is no clear evidence for systematic radial accretion inflows that alone could feed and sustain the star formation process in the inner regions of local spiral galaxies at its current rate.