AbstractA compressible viscous isothermal model is presented for studying journal‐bearing lubrication. The viscosity in the model thickens with increasing density. The governing equations are written in terms of velocity, the natural logarithm of the density and the kinematic extra‐stress tensor. A semi‐Làgrangian treatment of the material derivatives is combined with a spectral element discretization in space. The roles of the speed of sound and the eccentricity ratio on the load‐bearing capacity of the journal bearing are investigated. Compressibility is shown to enhance the load‐bearing capacity and this effect is amplified as the eccentricity ratio approaches unity. It is shown that for speeds of sound in the region of those of multigrade oils, the dominant component of the force on the journal acts along the line joining the centres of the bearing and journal and in the direction away from the narrow gap. Copyright © 2007 John Wiley & Sons, Ltd.