A model for transport in amorphous anodic oxide films was developed in which ion migration was driven by gradients of mechanical stress as well as electric potential and which included viscoelastic creep of the oxide. Simulations were presented for the galvanostatic growth of planar barrier-type anodic aluminum oxide films. It is assumed that stress originates at the metal-film interface due to the volume change upon oxidation. The average stress in the film decayed during growth and evolved from compressive to tensile with increasing applied current density. The model was fit to stress-thickness measurements using a viscosity of 1x10(12) Pa s on the same order of magnitude as that of many other amorphous materials displaying viscous creep. The current density increased exponentially with electric field, in agreement with an empirical high field conduction behavior. The metal ion transport number was predicted based on the motion of markers in the film and increased with current density in quantitative agreement with experimental measurements. The model represents a unified quantitative interpretation of ionic conduction, transport numbers, and mechanical stress measurements in anodic films.