The uptake of HCl on vapor-deposited ice is investigated for HCl partial pressure p from 2 x 10(-8) to 10(-5) Torr at temperatures of 190 and 203 K in an especially designed Knudsen cell experiment. Two kinetic regimes can be distinguished experimentally: a long-lasting tailing which accounts for the major amount of the overall uptake and follows diffusion-like kinetics, gamma(t) proportional to t(-1/2) (gamma, uptake coefficient; t, time), and an initial period, where the uptake is higher than predicted by diffusion-like kinetics. The uptake kinetics are analyzed using analytical equations and also by full numerical simulation of simultaneous adsorption onto the surface and diffusion into the bulk. We derive the quantity H-d*D-1/2 (H-d*, effective Henry's law constant, D diffusion constant) and find H-d*D-1/2 proportional to p(-1/2), which implies that HCl dissociates upon uptake. The results for both analysis methods closely coincide. We suggest the use of a semiempirical parametrization for the total HCl uptake (molecules per geometric surface area) on vapor-deposited ice films as time dependent function n(t, p) = n(resid)(P) + C(T)(tp)(1/2), where C(T) is a constant which depends on temperature only. The compatibility of the residual, nondiffusive uptake, n(resid), with various adsorption isotherms is discussed. The analysis suggests that the experimentally observed diffusion-like kinetics dominates the overall trace gas uptake after a brief initial period. The diffusion-like kinetics must be considered when analyzing uptake experiments and when making applications to natural ice.