We use numerical models to investigate the deformation associated with folding by hinge-zone migration. The model geometry consists of a layer that is displaced over a basal fault with a flat-ramp trajectory. The models use an elastic-plastic Mohr-Coulomb material that allows deformation to be localized as shear bands. Bedding can be simulated as discrete interfaces of slip or as weak layers within the continuum. Two orientations of shear bands are dominant: (1) back thrusts that initiate along the axial surface of the fold and (2) layer-parallel shear bands. The style of deformation in the models is controlled by material properties, degree and type of bedding anisotropy, and geometry of the basal fault. In models with homogeneous, isotropic, elastic–perfectly plastic material properties, shear strain rate is localized in a band along the axial surface that is fixed above the fault bend. A uniform region of high shear strain develops above the ramp in material that has moved through the active axial surface. With cohesion softening, deformation is accentuated in the high-shear-strain-rate band. The active shear band is fixed to the material and moves up the ramp, but its base is pinned to the fault bend. As a result, the band rotates until it reaches an unfavorable orientation relative to the local stress field; then it is abandoned as a new shear band propagates up from the fault bend. This mechanism produces a series of abandoned back-thrust shear bands above the ramp. The introduction of bedding-parallel anisotropy or a rounded fault bend causes layer-parallel shear bands to develop. With increasing anisotropy, there is a transition from back thrusting to layer-parallel shear. The layer-parallel shear bands initiate at the fold's axial surface, and the propagating tips of the bands remain at the axial surface while inactive parts of the bands are carried up the ramp. The models provide insight into the development of back thrusting and bedding-parallel slip, two mechanisms of hinge-zone migration that are common features in both natural structures and analog models.