We present results of classical trajectory (CT) calculations on the sticking of protons to the basal plane (0001) face of crystalline ice, for normal incidence at a surface temperature (T-s) of 80 K. The calculations were performed for moderately low incidence energies (E-i) ranging from 0.05 to 4.0 eV. Surprisingly, significant reflection is predicted at low values of E-i (≤ 0.2 eV) due to repulsive electrostatic interactions between the incident proton and the surface water molecules with one of their H-atoms pointing upward toward the gas phase. The sticking probability increases with E-i and converges to unity for E-i ≥ 0.8 eV. In the case of sticking, the proton is trapped in the ice forming a Zundel complex (H5O2+), with an average binding energy of 9.9 eV with a standard deviation of 0.5 eV, independent of the value of E-i. In nearly all sticking trajectories, the proton is implanted into the ice surface, with a penetration depth that increases with E-i. The strong interaction with the neighboring water molecules leads to a local rupture of the hydrogen bonding network, resulting in collision induced desorption of water (puffing), a process that occurs with significant probability even at the lowest E-i considered. The probability of water desorption increases with E-i. In nearly all trajectories in which water desorption occurs, a single three-coordinated water molecule is desorbed from the topmost monolayer.