Similar to the well-known neck propagation phenomenon, shearing of polymer materials often reveals the initiation and subsequent propagation of a shear band. Finite element analysis is used to numerically simulate large plane strain, simple shear tests, focussing attention on the initiation and propagation of the shear band. The mesh sensitivity and effects of initial imperfection, strain softening, orientation hardening, strain-rate as well as the edge effects are discussed in detail. It appears that the intrinsic softening is the driving force to promote initiation of the shear band and its propagation in the shear direction, while the orientation hardening is the driving force for widening of the shear band. The predicted numerical results are compared with experimental data for polycarbonate found in the literature.