As found by experiments quasi rate independent materials (QRI ) describe very well behavior of steels in very wide range of strains and strain rates ([3],[4]). This property has been combined with tensor representation modeling using a generalized associative flow rule based not on the yield function but on a more general loading function. Seemingly rate independent QRI producing incremental evolution equations show rate sensitivity by means of variability of yield stress with stress rate. On the other hand transverse isotropy appears in metal forming issues like in rolled car body sheets [18]. Here an extension of tensor generators and invariants is needed to include the preferred anisotropy direction. Such a procedure has been made here. In addition we believe that the results of this paper are applicable to dynamic deformation of orthogneiss rocks treated recently in [5].