Impinging liquid jets are widely used in industry to clean unwanted soil layers from the internal walls of storage tanks and mixing vessels. Viscoplastic layers are common in a wide range of industrial applications and are challenging to clean due to their yield stress behaviour. When a stationary coherent turbulent perpendicular liquid jet impinges on a flat soiled surface, it generates a roughly circular cleaned region that grows over time. In this work, different insoluble viscoplastic materials such as petroleum jellies and a white soft paraffin were cleaned by impinging water jets. The rheological investigation of the soil layers indicated that these materials show time-dependent yield stress behaviour. A method to measure the yield stress of soil layers in-situ using a blade-scraping device was developed and shown to provide reasonable estimates of the yield stress of different industrial ointments, household items and food spreads. Two distinct regimes were observed in cleaning experiments by impinging jets: for thin soil layers, the liquid film pushed the soil layer radially outwards in a momentum-driven flow. For very thin soil layers, the liquid film flowed over the soil layer. The transition between these two regimes is related to the relative thickness of the liquid film to the soil layer. A phenomenological model was proposed to describe the transition from fast, momentum-driven to slow, creep-dominated cleaning of thin soil layers, and provided good agreement with experimental results. It required the fitting of a kinetic constant to experimental data to describe the initial fast growth of the cleaned radius close to the impinging point. A detailed model was also developed based on the rate of viscous dissipation in a shallow wedge of material at the cleaning front, which explains the kinetic parameter used in previous models in the literature in terms of measurable quantities, including the rheology of the soil. A shear-driven model was also proposed to describe the cleaning of very thin soil layers. This model gave inconsistent results when compared to experiments, and it is proposed that this results from the model not coupling the flow between the soil layer and the liquid film.