The study of elastohydrodynamic (EHD) contacts is primarily concerned with the film thickness and the traction force developed between two, heavily loaded, solid surfaces in relative motion with each other. The aim of this paper is to calculate simultaneously film thickness, pressure, and shear stress distributions in isothermal EHD point contacts lubricated with a Ree–Eyring fluid under steady state conditions. A numerical method is developed to solve the EHD point contact problem for moderate and high loads. Theoretical results show that film thicknesses do not vary from those computed for a Newtonian fluid, except in the cases of very small values of the Eyring reference stress which lead to a significant reduction in film thickness. Calculated traction forces in rolling–sliding contacts are similar to those measured experimentally. The theory is compared with experiments made on a rolling–sliding point contact apparatus in which film thicknesses and traction forces are measured simultaneously. Good agreement is found.