Plastic anisotropy effects may be described in a phenomenological model by employing in the constitutive theory a set of internal variables, which are defined suitably. These variables have to model the hardening response of the material under consideration to describe e.g. the rotation of some symmetry axes. Such axes are imagined to be related with the development of the material substructure assumed, or, correspondingly, with the state variables characterizing this development. The objective of the first part of this work is to develop the constitutive equations governing the material response for the case of orthotropic and cubic anisotropy. Therefore the thermodynamically consistent theory for plasticity (and viscoplasticity), recently published by Tsakmakis (2004), which accounts for anisotropy effects is presented and extended for the aforementioned cases of anisotropy. Important features of the theory are the use of the multiplicative decomposition of the deformation gradient tensor as well as the assumption of the validity of Il'iushin's postulate in the case of plasticity. For simplicity, apart from kinematic hardening effects, only orientational evolution of the underlying substructure is regarded. Care is taken that the theory is invariant with respect to rigid body rotations superposed to both, the current and the so-called plastic intermediate configuration. Anisotropy effects are elaborated in the free energy and the yield function by means of structural tensors. For the case of cubic material symmetry a Brinell hardness indentation test has been simulated and is compared qualitatively with the experiment for a commercially available single-crystal nickel-based superalloy (CMSX4). Inelastic deformations induce anisotropy in the material response, even if this is initially isotropic. For metallic materials, deformation induced anisotropy is reflected, above all, by translation, rotation and distortion of the yield surface. This has been confirmed by several experimental investigations independent of the way the yield point is defined. In the second part of this work a simple, thermodynamically consistent model is proposed, describing the evolving anisotropy of the yield surface. The model is first theoretically established, based on a sufficient condition for the dissipation inequality to be satisfied. Then, it is applied to predict the subsequent yield surfaces, after various prestressings, which have been observed experimentally by Ishikawa for SUS 304 stainless steel.