A new phenomenological model is proposed to correlate extrudate expansion and extruder operation parameters in a twin-screw food extrusion cooking process. Buckingham's pi dimensional analysis method is applied to establish the model. Three dimensionless groups, i.e. pump efficiency, water content and temperature, are formed to model the extrusion process from dimensional analysis. The model is evaluated with experimental data for extrusion of whole wheat flour and fish feed. The average deviations of the model correlations are 5.9% and 9% based on experimental data for the whole wheat flour and fish feed extrusion, respectively. An alternative four-coefficient extrudate expansion equation is also suggested for the three dimensionless groups. The average deviations of the alternative equation are respectively 5.8% and 2.5% in correlation with the same set of experimental data.