Non-expert summaryImpinging liquid jets are widely used to clean unwanted soil layers from the walls of structures and vessels. This paper investigates what is observed when a coherent, turbulent, water jet impinges normally on a thin layer of an immiscible viscoplastic material. Removal involves the growth of a cleared area (which is circular for a jet impinging normally) bounded by a berm of displaced material. Previously Glover et al. [2016, J. Food Eng.. 178, 95-109] presented a semi-empirical model relating the rate of removal (location of the berm) to the momentum flow rate in the liquid film. The authors present a first-order model for cleaning thin layers of these materials based on the rate of viscous dissipation in a shallow wedge of material at the cleaning front. This yields a result of the form of the Glover et al. model, with expressions linking the kinetic parameters to measurable quantities including the rheology of the soil. The fully coupled problem is not solved: the wedge angle and residual layer thickness need to be specified and in this work they were obtained by fitting to the data. New and existing experimental results are compared with the model for three soft solids immiscible with water: two petroleum jellies and a soft paraffin, which exhibited Bingham plastic behaviour and creep, for jet Reynolds numbers between 10,000-37,000. The ratio of average film depth and layer thickness was in the range 0.1-1.5.