In the current work we present a finite visco-plasticity model accounting for inherent and induced plastic anisotropy as well as Bauschinger effect for the interstitial free (IF) steels and its application to a forming process simulation of DC06 sheets. The inherent plastic anisotropy uses a Hill-48 type structural tensor whereas the induced anisotropy is modeled via its evolution accounting for dynamic (active) and latent (inactive) parts. The latter appears to be an eminent requirement for predicting the qualitative effect of the evolving dislocation microstructures under orthogonal loading path changes, i.e., the cross hardening. A nonlinear isotropic and Armstrong-Frederick type kinematic hardening is also involved. Finally, the rate dependence of the plastic response is incorporated using Johnson-Cook type formulation. The model is implemented as VUMAT user defined material subroutine for ABAQUS and used in a set of sensitivity analyses to present mentioned model features. The model parameters are identified based on a set of experiments involving monotonic shear, uniaxial tension, forward to reverse shear and plane strain tension followed by shear tests. Finally, the channel forming process of a DC06 sheet is simulated. A good agreement with the experimental findings is observed, in both the tool response history curves and the extent of spring-back which is conclusive on the final product geometry.