A numerical solution of the elastohydrodynamic lubrication problem for pure rolling with non-Newtonian lubricants is outlined. The non-Newtonian rheological model used is a modified power-law tau equals K multiplied by (times) gamma **n. At low shear rate gamma less than gamma //b, the lubricant is Newtonian, but when gamma greater than gamma //b the lubricant becomes non-Newtonian, tau equals K multiplied by (times) gamma **n. At high shear rate ( gamma yields infinity ) the lubricant becomes Newtonian again with the same viscosity as the base lubricant. By using this rheological model a modified Reynolds' equation is derived. The influence of the n-value and gamma //b on the film thickness has been investigated. Plots of the pressure distribution and film thickness within the contact for fluids with G-values in the range 169-986 is presented. These G-values are typical for water-based hydraulic fluids. For fluids with low n-values (n less than 0. 5) the pressure profile approaches the Hertzian pressure distribution and the minimum film thickness is that given by the base fluid viscosity.