Water channels are formed in highly permeable thief zones or in situations with a strong adverse mobility ratio, such as waterflood in heavy oil reservoirs. This paper discusses the effect of tertiary polymer injection on oil mobilization in already established water channels generated by viscous unstable flow in apparent homogeneous rock material. Polymers may accelerate oil production by moving oil into water channels, known as crossflow. The conditions for crossflow to occur are discussed and quantified by key parameters for maximizing crossflow. Crossflow in layered rock with permeability contrast has been studied extensively. We have also studied permeability contrast in conventional thief zones for comparison. Recently published experimental studies, including in situ saturation maps, have proven acceleration of heavy oil production by injection of polymer in rather homogeneous sandstones. The simulation study involves computation of saturation-inauced crossflow, in particular with respect to wettability, relative permeability hysteresis, capillary pressure, oil viscosity, mobility ratio, and polymer viscosity. To have a realistic representation of channeling, the water channels are constructed from waterflooding saturation data at adverse mobility. Saturation-induced crossflow into water channels at homogeneous permeability is found to be strongly affected by wettability, viscosity ratio (oil/water), and width of water channels.