AbstractTwo‐phase, annular flow of gases and non‐Newtonian liquids through horizontal pipes is modeled, and a prediction method for pressure drop and gas volume fraction is proposed. The prediction method consists of a modification, based upon shear rate dependence of the apparent viscosity of the liquid phase, of Lockhart‐Martinelli correlations for Newtonian liquids. The model applies to the case of laminar flow of the annular liquid film. Experimental data, obtained with several aqueous polymer solutions and air, agree closely with predicted values of pressure drop and void fraction.