The mechanical response of extruded and injection molded semicrystalline materials, in which an oriented microstructure is commonly observed, depends on the direction of loading. Plastic deformation and failure are, therefore, both anisotropic. The ability of a micromechanical model, including the characterization of the kinetics of crystallographic slip and amorphous yield, to describe the yield kinetics of oriented high-density polyethylene tapes with different draw ratios is evaluated here. The initial morphology of the material is characterized with wide-angle X-ray diffraction experiments, which evidence a strong alignment of molecular chains with the drawing direction for specimens produced with a large draw ratio. Anisotropic crystal plasticity alone in a two-phase framework proves not able to quantitatively describe the macroscopic mechanical response in the solid state hot drawn samples. Most likely, these deviations are related to process-induced orientation within the amorphous domains. Therefore, the influence of loading angle dependent yield kinetics for the amorphous phase is evaluated, and indeed the description improves considerably. Finally, the possibilities for characterizing the properties of different crystallographic slip systems are discussed.