Cyclic loading induced foundation instabilities including 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 were limited studies on the modelling of cyclic loading of soft soils due to its complexities compared to static loading. In this study, a model for soft clays under partially drained condition subject to cyclic triaxial loading has been developed based on the Modified Cam-clay theory. The yield surface contraction for elastic unloading was governed by two additional cyclic degradation parameters to the modified Cam-clay model. This model was validated using the results of a series of undrained and partially drained cyclic triaxial loading tests on kaolin. A good agreement between the numerical prediction and the measured excess pore pressures was obtained. Furthermore, the factors which influence the cyclic performance of soft soils, e.g. the cyclic stress ratios, the anisotropic consolidation stress and the coefficient of consolidation were investigated. This model was then applied to the consolidation of soft soils under cyclic loading, which represents the application of partially penetrated vertical drains for road and rail infrastructure, at the soft soil sites for a rail project in Sandgate, NSW. The objective of the partially penetrated drains within this deep estuarine soil layer was to consolidate the shallow soft clays and stabilise the new built tracks.