We present systematic molecular dynamics simulation studies of hydrogen storage in single walled carbon nanotubes of various diameters and chiralities using a recently developed curvature-dependent force field. Our main objective is to address the following fundamental issues: 1. For a given H-2 loading and nanotube type, what is the H-2 distribution in the nanotube bundle? 2. For a given nanotube type, what is the maximal loading (H-2 coverage)? 3. What is the diameter ranae and chirality for which H-2 adsorption is most energetically favorable? Our simulation results suggest strong dependence of H-2 adsorption energies on the nanotube diameter but less dependence on the chirality. Substantial lattice expansion upon H, adsorption was found. The average adsorption energy increases with the lowering of nanotube diameter (higher curvature) and decreases with hi-her H, loading. The calculated H-2 vibrational power spectra and radial distribution functions indicate a strong attractive interaction between H-2 and nanotube walls. The calculated diffusion coefficients are much hiaher than what has been reported for H-2 in microporous materials such as zeolites, indicating that diffusivity does not present a problem for hydrogen storage in carbon nanotubes.