In this paper, density functional theory is used to estimate hydrogen adsorption in a novel carbonaceous material, single-walled carbon nanotubes. An idealized adsorbent structure for the nanotubes is assumed. We have mapped out the regime of operating pressures and temperatures where an adsorption-based storage system is expected to deliver more hydrogen than a similar system of compressed gas. This regime is also a function of pore size. We have calculated the overall hydrogen volumetric and gravimetric density within the framework of a typical high-pressure gas storage system. Within the regime of operating conditions where adsorptive storage seems attractive, the storage properties of hydrogen in a carbon nanotube system appear to fall far short of the targets of 62 kg of H-2/m(3) and 6.5 wt % H-2 set by the Department of Energy. The computed gravimetric storage densities also fall short of those reported in the literature (Nature 1997, 386, 377). We discuss several possible mechanisms by which higher gravimetric density could be rationalized, including chemisorption, adsorption at interstitial sites, and swelling of the nanotube array.