In this article, we demonstrate how the non ionic polymer, the polyethylene oxide (PEO) with molecular weight 6000 g/mol of varying concentration mass (0.7%, 1%, 2% et 3%) significantly alter the rheological properties (yield stress, viscosity, loss and elastic modulus) of the bentonite suspensions (6%) in the water. The different rheological tests made in simple shear and in dynamic on the ternary system (water-bentonite-PEO), showed the influence of the polymer on the rheological properties of this drilling fluid. The PEO which presents an affinity for the bentonite particles slows down the kinetic of aggregation of the clay particles. Also the analysis by X-rays diffraction on different samples revealed the intercalation of the clay platelets on one hand and the links bridges assured by the chains of polymer between bentonite particles beyond a critical concentration in PEO on the other hand. The Herschel-Bulkley rheological model is used for the correlation and the interpretation of our experimental results.