A model is proposed for the formation of water ice mantles on grains in interstellar clouds. This occurs by direct accretion of monomers from the gas, be they formed by gas or surface reactions. The formation of the first monolayer requires a minimum extinction of interstellar radiation, sufficient to lower the grain temperature to the point where thermal evaporation of monomers is just offset by monomer accretion from the gas. This threshold is mainly determined by the adsorption energy of water molecules on the grain material; for hydrocarbon material, chemical simulation places this energy between 0.5 and 2 kcal mol−1, which sets the (true) visible extinction threshold at a few magnitudes. However, realistic distributions of matter in a cloud will usually add to this an unrelated amount of cloud core extinction, which can explain the large dispersion of observed (apparent) thresholds. Once the threshold is crossed, all available water molecules in the gas are quickly adsorbed, because the grain cools down and the adsorption energy on ice is higher than on bare grain. The relative thickness of the mantle, and, hence, the slope of τ3(Av) depend only on the available water vapour, which is a small fraction of the oxygen abundance. Chemical simulation was also used to determine the adsorption sites and energies of O and OH on hydrocarbons and study the dynamics of formation of water molecules by surface reactions with gaseous H atoms, as well as their chances to stick in situ.