A mathematical model was developed for ionic conduction in amorphous oxide films. The model is based on a hypothesized "defect cluster" mechanism in which both metal and oxygen ions are involved in transport. Defect clusters are created by inward displacement of oxygen ions around an oxygen vacancy-like defect in response to the vacancy's electric field. Metal ions are assumed to migrate easily in the gap between the first and second layer of oxygen ions around the vacancy. The model includes the polarization of the conductive gap in the applied electric field, the exchange of mobile metal ions in the cluster with stationary metal ions in the surrounding oxide, and space charge generated in the film by clusters and oxide nonstoichiometry. The rate-limiting step is the jump of the oxygen vacancy in the cluster. It was found that polarization of the cluster leads to a stoichiometric excess of metal ions in the cluster and that this excess produces a net transport of metal ions due to the motion of the cluster. The metal ion transport number was found to increase with electric field and to depend on the dielectric constant and cluster size. The field dependence follows that found experimentally. The calculated transport numbers are in quantitative agreement with experimental values for tantalum, niobium, and tungsten oxide but smaller than experimental values for aluminum oxide. The field coefficient in the high-field-conduction-rate expression is also predicted and agrees with experimental values to within 10%.