Classical trajectory methods are used to examine the trapping and sticking of H and D atoms on the graphite (0001) surface. Total energy calculations based on density functional theory are used to construct the model potential energy surface, and graphite clusters of up to 121 atoms are considered. For hydrogen to chemisorb, the bonding carbon must pucker out of the surface plane by roughly 0.4 A. For incident energies above the 0.2 eV barrier, any trapped H atoms must rapidly dissipate their excess energy into the surrounding lattice within a few vibrations of the C-H stretch in order to remain bound. For sufficiently large clusters, the C-H bond stabilizes within about 0.1 ps. The sticking probability for D at 150 K is in the range of 5%-10%, more-or-less consistent with the most recent measurements in the limit of zero coverge. Variation with isotope and substrate temperature is weak. We estimate that the sticking cross section for adsorption at the para site, directly across the sixfold carbon ring from an already adsorbed H atom, can be four or more times larger that the zero coverage sticking cross section.