An oil based drilling mud is viscosified with a maleated ethylene-propylene elastomers. The elastomers are preferably EPM copolymers or EPDM terpolymers. The concentration of the maleic anhydride grafted to the copolymer or terpolymer backbone ranges from 0.01 to 5 wt %, preferably 0.1 to 2.0 wt %. The maleated elastomers are far more effective oil mud viscosifiers than the organophilic clays presently used.