The major problems associated with shale formation when it interacted with water based mud are borehole instability. This Wellbore instability may be due to swelling and dispersion of clay present in shale and also leads to other well problems like pipe sticking, hole enlargement, improper rheological & fluid loss control properties, and additional reaming etc. In this research paper an attempt has been made to evaluate the feasibility of synthesized graft copolymer in the formulation of water based mud system for challenging formations. The microwave irradiation technique has been adopted for synthesizing PAA/AMPS-g-Sesbania gum copolymer. Further, it was processed in the formulation of mud system. The remarkable rheological and filtration properties of the mud system have been seen with synthesized additive. The developed mud has possessed strong pseudoplastic behavior which is a desired property of any mud which has been observed from shear rate vs. shear rate curve. In addition, shale stabilization properties were investigated with shale rotability test on the synthesized core sample prepared in the laboratory. Moreover, percentage reduction in permeability (i.e., formation damage effect) has been found lesser in developed copolymer system co paring to conventionally used PHPA system. Hence, the formulated mud system can be used as a potential drilling mud system for drilling any oil wells.