The isotropic finite viscoplasticity theory based on overstress (FVBO) is extended to anisotropy. It is accomplished by formulating an anisotropic flow law, which consists of a fourth order inelastic compliance tensor. Since large inelastic deformation causes a change in the microstructure, the aforementioned tensor is allowed to evolve according to the Frederick-Armstrong type law during inelastic deformation. Additive decomposition of the rate of deformation into elastic and inelastic parts is assumed. The current configuration is taken as a reference configuration. (C) 2004 Elsevier Ltd. All rights reserved.