For the FE simulations relying on elasto-plastic models based on anisotropic yield locus description, it is important for the simulation accuracy to follow a Cartesian reference frame, where the yield locus is expressed. The classical formulations like the Hill 1948 model keep a constant shape of the yield locus when other texture based yield loci regularly update their shape. However in all these cases, the rotation of the Cartesian reference frame must be known. For simple shear tests performed on steel sheets, experimental displacements provide the actual updated position of initial orthogonal grids. The initial and final texture measurements give information on the average crystals rotation. For Hill constitutive law and texture based models, this paper compares the experimental results with different ways to follow the Cartesian reference frame: the co-rotational method, an original method based on the constant symmetric local velocity gradient and the Mandel spin computed by four different methods.