A mathematical model was developed to describe the juice expression process from a saturated bed of a solid-liquid system. The model was based on a fundamental mass balance. The cake permeability was considered dependent on bed porosity which itself was described as an empirical function of pressure. The cake deformation was accounted for by considering the juice expression to be a moving boundary problem. The model was solved on a digital computer by a finite difference numerical technique. Carrot pulp was pressed in a test cylinder at three pressures (1.15, 2.31 and 3.46 MPa) and different pressing times up to 20 min. Darn on juice recovery and cake deformation were collected to validate the model. The experimental data for juice recovery were used to estimate the parameters of the model using non-linear parameter estimation. The model predictions of juice recovery and cake deformation compared satisfactorily with the experimental data.