Blends of sorghum and cowpea flour (10%, 20% and 30%) were extruded at 20%, 22.5% and 25% moisture and 120 °C, 140 °C and 160 °C barrel temperatures respectively, using a single-screw extruder. A central composite face-centered (CCF) design was used to model the specific power consumption (SPC), torque, mass flow rate (MFR) and apparent specific volume (ASV) of the sorghum–cowpea extrudates. The SPC, torque, MFR and ASV varied from 201.71 to 229.28 Kw h−1 kg−1, 85 to 97 Nm, 1.94 to 2.31 g s−1 and 4.01 to 6.36 cm3, respectively. The SPC was significantly (p<0.05) influenced by the linear effect of feed composition and the interaction effects of feed moisture and extrusion temperature. The torque was however significantly (p<0.05) influenced by the linear effect of feed moisture and the interaction effects (p<0.01) of feed moisture and extrusion temperature. The ASV was significantly (p≤0.01) influenced by the linear effect of extrusion temperature and the quadratic effect of extrusion temperature as well as the interaction effects of feed composition and feed moisture. The coefficients of determination were 0.78, 0.79, 0.63 and 0.86 for SPC, torque, MFR and ASV, respectively. There was no significant lack of fit for the SPC, torque, and MFR of the extrudates. The correlation coefficients (r2) for the observed and predicted values were 0.88, 0.75, 0.78 and 0.93 for SPC, torque, MFR and ASV, respectively, indicating a good fit for the model. The CCF was found appropriate in predicting the SPC, torque, MFR and ASV of the extrudates.