In this paper an approach is proposed to account for Generalised Newtonian lubrication flow in a lubricated bearing geometry. The approximate approach solves the lubricant viscosity accross the lubricated gap, the coefficients in the equation describing the viscosity across the gap are then solved for iteratively. This permits an approximation of the lubrication equation to be arrived at which considers the Poiseuille components of the flow as well as the Couette terms. The reduction in error of around 30-40% is observed in the bearing pressure field for the cases considered here. © 2012 W. S. Maney & Son Ltd.