Cyclic loading induced foundation instabilities such as the loss of bearing capacity and excessive plastic deformation of the subgrade are among the major concerns for the design and construction of transport infrastructure. There are limited studies on the modelling of cyclic loading of soft soils due to its complexities compared to static loading. In this study, a new constitutive model for soft clays under undrained cyclic triaxial loading has been developed based on the Modified Cam-clay theory. A new yield surface for elastic unloading was introduced by adopting two additional cyclic degradation parameters, which govern the change of the yield surface when unloading. Based on the proposed model, a numerical model is introduced to determine the effective stresses and strains. The proposed model was validated using the results of a series of undrained cyclic triaxial loading tests on kaolin. A good agreement between the numerical prediction and the measured excess pore pressures and axial strains was obtained. Furthermore, the factors which influence the cyclic performance of soft soils, e.g. the frequency, cyclic stress ratios and anisotropic consolidation stress, were investigated. The critical cyclic stress ratio can also be predicted by using the proposed model in terms of the excess pore pressures and axial strains. This theory was then applied to the combined vertical and radial consolidation of soft soils under cyclic loading, which represents the application of partially penetrated vertical drains for road and rail infrastructure at soft soil sites for a rail project in Sandgate, NSW. The objective of the partially penetrated drain within this 30 m deep estuarine soil was to consolidate the shallow soft clay layer underneath the track.