A unified modelling theory for the prediction of the pressure drop of non-Newtonian purely viscous flow through isotropic high porosity synthetic foams is proposed. The model is derived by volumetrically averaging the equations of motion over an arbitrary two-phase system of stationary solids and a traversing fluid. Closure is obtained by using a formerly introduced rectangular representation of the pore space morphology. The shear rate dependency of the viscosity is incorporated through the sheer stress in terms of the power-law model. The proposed model, which is based purely on physical principles with no artificial adjusting parameters, is compared to other predictive models in terms of friction factor as a function of the Reynolds number. Predicted pressure drop results are also compared to published experimental results to verify the validity of the model.