The flow stress behavior of a bake-hardenable steel during a few simple shear cycles is investigated using a crystal plasticity model. The simple shear test provides a stable way to reverse the loading direction. Stress reversals were accompanied with a lower yield stress, i.e., the Bauschinger effect, followed by a transient hardening stage with a plateau region and, permanent softening. The origins of these three distinct stages are discussed using a crystal plasticity model. To this end, the representative discrete grain set is tuned to capture such behavior by coupling slip system hardening appropriately. The simulated results are compared with experimental forward-reverse simple shear stress-strain curves. It is shown that the characteristic flow stress stages are linked to texture evolution and to the Bauschinger effect acting on the different slip systems.