Shear banding is an outstanding problem in lubricant rheology where a thin film of lubricant is under high pressure and high shear stress. To study such a phenomenon, a viscoelastic-plastic model is proposed. It is postulated that shear bands appear when the character of the field equations changes from elliptic to hyperbolic. The model is derived based on a rate formulation which combines a Maxwell fluid model and a compressible rate-independent plasticity model. The model gives the constitutive relation of a compressible viscoelastic-plastic fluid for which the assumption of Stokes condition becomes unnecessary. It also accounts for the elastic coupling effect of both the viscous and the rate-independent behavior of a lubricant. It provides a novel feature that the development of shear bands can be tracked rather than being determined after they are fully developed. Hence, the process of shear banding may be articulated. The analysis focuses on identifying necessary and sufficient conditions which, if achieved in a deformation, would produce a change in character of the governing field equations. Through the use of Drucker-Prager criterion as the component that governs the rate-independent behavior of a lubricant, the analysis gives results that are in accord with experimental observations. Parametric results are given graphically.