Shear localization has been observed in liquid lubricants flowing at high pressure. Two kinds have been identified: for stress-controlled plane Couette shear at high values of Nahme No., thermal runaway can result in the appearance of a band at mid-plane where the temperature and shear rate become localized. Alternatively, at high pressure and high shear stress, intermittent slip can be visualized along inclined bands for both planar Couette shear and squeeze film flows. These mechanical shear bands are responsible for the rate independent behavior that characterizes the traction transferred across the lubricant film in concentrated contact. We consider three models for shear band formation: Mohr–Coulomb slip, loss of ellipticity of Navier–Stokes equations, and non-monotonic stress–strain rate response. The observations that slip occurs for a ratio of shear to normal stress of about 0.1 and that bands form in two characteristic directions support both the Mohr–Coulomb failure criterion description and a change of character of the governing differential equations. Some evidence of constitutive instability is also presented; however, band orientation does not support this model.