A model of two-phase non-Newtonian horizontal annular flows, which predicts film thickness and pressure gradient from flowrates only, is presented. In the model, the gas and non-Newtonian liquid flows are calculated separately based on the independent governing equations. The shear stress balance at the gas-liquid interface is calculated in order to link two phases together. The non-Newtonian fluid is assumed as a power-law shear-thinning liquid. The logarithmic velocity distribution is chosen to calculate the turbulent velocity profile in the gas core. The influences of entrainment and aeration are included in the model. The pressure drop, film thickness, void fraction, the frictional multiplier, and Lockhart-Martinelli parameter are predicted. The analytical model is compared with the published experimental investigations, and the results show that the model can predict the film thickness and pressure gradient simultaneously based on the flowrates of liquid and gas. The frictional multiplier and Lockhart-Martinelli parameter are calculated at the same time, and the predicted values are comparable with the experimental data The difference between the analytical model and the experiments is lower than 10%. (C) 2013 Elsevier Ltd. All rights reserved.