Impinging liquid jets are widely employed in cleaning operations to remove residual soiling layers from walls and other surfaces of process vessels. Insoluble viscoplastic soiling layers represent challenging soils to clean as removal is primarily by hydraulic forces. The rheological behaviour of a commercial petroleum jelly was investigated and shown to exhibit significant creep below its critical stress. The removal of thin (< 1 mm) layers of petroleum jelly from glass and Perspex surfaces by coherent water jets impinging normally on vertical walls were studied experimentally. The jet clears a roughly circular area, forming a berm of removed material at the cleaning front. The shape of the berm was measured and found to depend on the ratio of the height of the water film and the initial thickness of the soil layer. The data were compared with the adhesive removal of viscoplastic soils proposed by Glover et al. (J. Food Eng., 2016, 178, 95-109) with the momentum flow rate calculated using the results in Bhagat and Wilson (Chem. Eng. Sci, 2019, 152, 606-623). The asymptotic approach to a cleaning limit observed in experiments with static nozzles required modification of the model: a semi-empirical term which represents the transition to a creeping regime is presented. The modified model allowed results obtained using static nozzles to predict the shape of the region cleaned by a jet from a similar nozzle moving across a soiled plate. The influence of process conditions on model parameters is discussed.