?????We have carried out a study of the distribution and kinematics of the neutral hydrogen in the direction of the Vela supernova remnant (SNR). A field of 68 ? 54 centered at l = 2641, b = -16 was surveyed using the Parkes 64 m radio telescope (half-power beamwidth 147 at 21 cm). Nearly 2300 H I profiles were obtained with a grid spacing of 75. The presence of a thin, almost circular H I shell, centered at v = 1.6 ? 0.8 km s-1, is revealed. This shell delineates the outer border of the X-ray emission as shown in the ROSAT observations of Aschenbach, Egger, & Tr?mper and wraps around the receding part of the remnant. In addition, two higher velocity features possibly associated with Vela are observed at about -30 and 30 km s-1. These features are interpreted as gas accelerated by the expansion of the supernova shock. The low systemic velocity observed suggests a distance shorter than 500 pc for the Vela SNR. The H I shell is ~7? in diameter and expands at v ~ 30 km s-1. By assuming a distance of 350 pc, we calculate for this shell a linear radius of 22 pc, a swept-up mass of ~1200?2300 M?, and an atomic preshock density of ~1?2 cm-3. The kinetic energy transferred by the supernova shock into the interstellar medium is ~(1?2) ? 1049 ergs, while the initial energy of the explosion is estimated to be ~(1?2.5) ? 1051 ergs. We present the distribution of the column density of the neutral material absorbing the X-radiation, an essential parameter in the analysis of X-ray data. A comparison between the H I and H? emission suggests that the H I shell contains embedded dust that might be responsible for increased optical absorption in this region. On the other hand, the brightest arc-shaped optical filaments associated with the western side of Vela show good correspondence with the H I features. From a comparison between the H I and Molonglo Observatory Synthesis Telescope 843 MHz radio continuum emission, we find that the outermost arched radio filaments correlate well with the main ridge of the H I shell. No strong inhomogeneities were found in the ambient H I medium in the direction of Vela X (the central nebula, powered by the pulsar PSR B0833-45).