A kinetic model is proposed for the absorption of water in polymers. The process of bonding-debonding water molecules is described by two opposite reactions with different rate constants, and the key role of the concentration of traps by hydrogen bonding in the polymer matrix is highlighted. These three parameters are combined such that an equation is obtained that generalizes the model proposed by Carter and Kibler, with an additional, crossed, term. Numerical application is performed for the diffusion-absorption of water in a plane polymer sheet, and the parameter ranges where a quasi-Fickian water uptake curve is obtained are defined. The associated apparent diffusivity is shown to obey a hyperbolic variation with equilibrium water uptake for homologous series of polymers, which is in agreement with previous experimental observations.