In this study, a pressure filtration model for a slurry of milk fat crystal aggregates is developed, validated and used to investigate the effect of pressure-time profiles. The model focuses on the expression step and describes oil flow locally. The filter cake is modelled as a double porous non-linear elastic medium with permeabilities described by the relation of Meyer & Smith. Conservation equations lead to a coupled system of differential equations, which are numerically solved exploiting a finite-difference scheme. Simulations with the model give insight through graphs of volume fractions versus filter chamber location at any given time step. Diagrams of oil outflow velocities and solid fat content of produced filter cakes show qualitatively good behaviour when compared to experiments. Studying the effect of pressure-time profiles, the model predicts that a low rate of pressure increase gives the driest filter cakes. Simulations also indicate that putting steps in pressure-time profiles is hardly effective.