A true (cubical) triaxial tester was built to study the three-dimensional load response of dry cohesionless and cohesive food powders at low pressures. The cubical triaxial tester was calibrated and used to load samples of wheat flour along isotropic, deviatoric and mean effective stress paths. Using results from isotropic, i.e., hydrostatic triaxial compression (HTC), tests, the critical state parameters were evaluated, namely, the modified Cam clay constitutive parameters lambda (loading slope) and kappa (unloading-reloading slope). Deviatoric and mean effective stress test results were used to evaluate the slope of the critical state line, M. Test results yielded lambda = 0.046, kappa = 0.011 and M = 0.98. The modified Cam clay constitutive model was verified by comparing the model predicted stress-strain behavior of powder with the cubical triaxial tester experimental data. The mean average relative difference (ARD) and mean absolute difference between measured and predicted curves for : (i) deviatoric stresses under conventional triaxial compression (CTC) stress path were 20.7% and 6.1 kPa, respectively; (ii) volumetric strains under CTC stress path were 50.3% and 1.2%, respectively; (iii) deviatoric stresses under mean effective stress (MES) test path were 15.7% and 5.6 kPa, respectively; (iv) volumetric strain under MES test path were 22.4% and 0.4%, respectively; and (v) voids ratio under HTC test path were 0.07% and 7 X 10(-4), respectively.