In dredging, high pressure water jets are commonly applied to assist the mobilization of soil. This work considers the excavation of cohesive soil. The key objective is to predict the development of the cavity in the soil as a function of the undrained shear strength, translation velocity and hydrodynamic pressure of a single nozzle. A generic computational fluid dynamics (CFD) model has been developed that captures both the jet flow and the soil failure in a single framework. The results are compared with data from a previous experimental study. The CFD model predicts the cavity dimensions with reasonable accuracy. In addition the model provides detailed data to study the cyclic nature of the soil failure process. The CFD model is promising and can be applied for more complex nozzle configurations to assist the design process of dragheads and improve production estimates.