New high-resolution, high-sensitivity Westerbork Synthesis Radio Telescope Hi synthesis observations of the spiral galaxy NGC 3631 are presented. In the total atomic hydrogen map, the spiral arms are well distinguished from the interarm regions, while the sensitivity allows detection of Hi in all but a few isolated regions of the areas between the spiral arms. Most of the atomic hydrogen is located within the optical disc, but the Hi extends to some 1.5R_opt. The Hi follows the spiral arms, and streaming motions of up to ~15 km s^-1 (projected) can be identified from the velocity field. Assuming a constant inclination angle of 17 deg, a rotation curve is derived which is declining slightly in the outer parts of the disc. An analysis of a residual velocity field, obtained after the subtraction of an axisymmetric model based on the rotation curve, confirms the existence of streaming motions near the spiral arms in an otherwise undisturbed disc.