In this paper the drag-out problem for shear-thinning liquids at variable inclination angles is considered. For this free boundary problem dimension-reduced lubrication equations are derived for the most commonly used viscosity models, namely, the power-law, Ellis, and Carreau model. For the resulting lubrication models a system of ordinary differential equations governing the steady state solutions is obtained. Phase plane analysis is used to characterize the type of possible steady state solutions and their dependence on the rheological parameters.