Water transport through soft contact lenses (SCL) is important for acceptable performance on the human eye. Chemical-potential gradient-driven diffusion rates of water through SCL materials are measured with an evaporation-cell technique. Water is evaporated from the bottom surface of a lens membrane by impinging air at controlled flow rate and humidity. The resulting weight loss of a water reservoir covering the top surface of the contact-lens material is recorded as a function of time. New results are reported for a conventional hydrogel material (SofLens One Day, hilafilcon A, water content at saturation w10 = 70 weight %) and a silicone hydrogel material (PureVision, balafilcon A, w10 = 36%), with and without surface oxygen plasma treatment. Also, previously reported data for a conventional 2-hydroxyethyl methacrylate (HEMA)-SCL (w10 = 38%) hydrogel are reexamined and compared with those for SofLens One Day and PureVision hydrogels. Measured steady-state water fluxes are largest for SofLens One Day, followed by PureVision and HEMA. In some cases, the measured steady-state water fluxes increase with rising relative air humidity. This increase, due to an apparent mass-transfer resistance at the surface (trapping skinning), is associated with formation of a glassy skin at the air/membrane interface when the relative humidity is below 55-75%. Steady-state water fluxes are interpreted through an extended Maxwell-Stefan diffusion model for a mixture of species starkly different in size. Thermodynamic nonideality is considered through Flory-Rehner polymer-solution theory. Shrinking/swelling is self-consistently modeled by conservation of the total polymer mass. Fitted Maxwell-Stefan diffusivities increase significantly with water concentration in the contact lens.