Interaction energies and entropies associated with hydrogen adsorption on the inner and outer surfaces of zigzag single-wall carbon nanotubes (SWCNT) of various diameters are analyzed by means of molecular mechanics, density functional theory, and ab initio calculations. For a single molecule the strongest interaction, which is 3.5 greater than that with the planar graphite sheet, is found inside a (8,0) nanotube. Adsorption on the outer surfaces is weaker than that on graphite. Due to the steric considerations, both processes are accompanied by an extremely strong decline in entropy. Absence of specific adsorption sites and weak attractive interaction between hydrogen molecules within carbon nanotubes results in their close packing at low temperatures. Using the calculated geometric and thermodynamic parameters in Langmuir isotherms we predict the adsorption capacity of SWCNTs at room temperature to be smaller than 1 wt % even at 100 bar.