An inhibitive water-based polymer mud system and method for using the system in drilling and in stabilizing wellbores is disclosed for use in water sensitive formations as an alternative to oil-based muds. The system comprises a substantially non-ionic low molecular weight polyacrylamide in combination with a substantially non-ionic high molecular weight polyacrylamide, preferably long chain alcohol or an amine or silicate shale inhibitor, and poly anionic cellulose.