Monte Carlo simulations and Widom's test particle insertion method have been used to calculate the solubility coefficients (S) and the adsorption equilibrium constants (K) in single-walled (10,10) armchair carbon nanotubes including single nanotubes, and nanotube bundles with various configurations with and without alkali dopants. The hydrogen adsorption isotherms at room temperature were predicted by following the Langmuir adsorption model using the calculated constants S and K. The simulation results were in good agreement with experimental data as well as the grand canonical Monte Carlo simulation results reported in the literature. The simulations of nanotube bundle configurations suggest that the gravimetric hydrogen adsorption increases with internanotube gap size. It may be attributed to favorable hydrogen-nanotube interactions outside the nanotubes. The effect of alkali doping on hydrogen adsorption was studied by incorporating K+ or Li+ ions into nanotube arrays using a Monte Carlo simulation. The results on hydrogen adsorption isotherms indicate hydrogen adsorption of 3.95 wt% for K-doping, and 4.21 wt% for Li-doping, in reasonable agreement with the experimental results obtained at 100 atm and room temperature.