Large-scale cyclic triaxial tests are conducted on remoulded kaolin specimens with 300 mm diameter and 600 mm height. To achieve radial drainage during and after the cyclic tests, a single prefabricated vertical drain (PVD) is installed in the centre of the soil cylinder. The test results verify that radial drainage can effectively dissipate the pore water pressure induced by cyclic loads. A radial consolidation model under cyclic loading is proposed to capture the behavior of soft clays subjected to cyclic loading when radial drainage is allowed during the loading and rest periods. It is achieved by combining radial consolidation theory with an undrained cyclic loading model. The effects of the stress history and dissipation of pore water pressure on the generation of pore water pressure are considered in the proposed model, which is verified by large-scale cyclic triaxial tests. It is found that for a high cyclic stress load, the radial drainage decreases the cumulative rate of pore water pressure up to the critical value, so the soil could undergo more loading cycles prior to failure. With a moderate cyclic stress load, the radial drainage prevents the pore water pressure from accumulating to the critical value. Furthermore, the effect of rest period on the generation of pore water pressure is investigated. It is indicated that the cumulative pore water pressure begins to decrease after three sets of cyclic loading, showing that no substantial pore water pressure will be observed if more sets of cyclic loading are applied.