Different shear-thinning and elastic fluids (STE fluids) have been stirred under unaerated conditions, in vessels equipped with Rushton disc turbines. Their power consumption has been evaluated over a wide range of stirring rates and their Metzner-Otto constant (k(s)) has been measured. A correlation has then been proposed to predict ks values for a Rushton turbine operating in non-Newtonian solutions. Power curves of STE fluids have been drawn and compared with reference curves (Newtonian, shear-thinning inelastic and elastic with constant shear viscosity fluids). The STE fluids have thus been divided into two categories. The STE fluids of the first category (STE I fluids), which are concentrated viscous solutions of polymers (guar, CMC) reducing the power consumption at the beginning of the transitional region and connecting with the Newtonian reference at higher Reynolds numbers. In contrast, STE solutions of the second category (STE II fluids), which are solutions of drag reducing polymers (PAA), are less viscous and more elastic. They reduce the power consumption at the end of the transitional region and do not connect with the Newtonian reference, at least until Re = 6000. A general correlation has finally been proposed to model the power curve of STE fluids stirred by a Rushton turbine from the laminar to the turbulent regions, as a function of their elasticity.