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 fresh water or salt water base thinned or dispersed with a water soluble, biodegradable polyamide-based copolymer having at least one grafted side chain formed from ethylenic unsaturated compounds. This system is effective and has stable rheology over a broad pH range, even at a near neutral pH of 8.0. The drilling fluids do not contain heavy metals and are rheologically tolerant to contaminants such as cement, anhydrite and sodium and temperatures as high as about 400° F.