Using the fact that for simple fluids the most general constitutive equation in constant stretch history flows for the extra stress tensor tau is known in an explicit form, the Giesekus fluid model is cast into this (omega-D) form for two-dimensional flows. The three material functions needed to characterize tau are listed. The explicit results for simple shear and planar elongation reveal that the parameter a should be restricted to values less than 0.5. It is demonstrated that in this explicit form the constitutive equation is free from thermodynamic objections and can thus be used as a starting point for numerical calculations of general, but steady, two-dimensional flows.