Soil compaction can be predicted in real-time by measuring the draught of a cutting tool, when the depth is held constant by the three-point hitch position control system of the tractor. A semi-analytical model was developed for the conversion of the voltage applied to the hydraulic subsystem of an agricultural tractor to the depth under the soil surface of an attached cutting tool (subsoiler) for online measurement of spatial variation in soil compaction. The model consisted of two distinct submodels: a model for the agricultural tractor based on a kinematic and dynamic analysis of the tractor in the XY plane and a `grey box' model for the hydraulic subsystem. The order of this `grey box' model was determined using a theoretical, mechanistic approach, while the parameters for the model structure have been determined using data-based modelling techniques. Both submodels have been coupled and successfully validated by comparing experimental results with those predicted by the model. It is concluded that the tractor dynamics are not excited by the activity of the hydraulic subsystem, when the subsoiler is attached. Therefore, a reduced model consisting of the hydraulic subsystem model multiplied by a conversion factor was found to be appropriate for the design of a depth controller for the soil compaction sensor. (C) 2004 Silsoe Research Institute. All rights reserved Published by Elsevier Ltd.