John Francis Brady (born January 8, 1954) is an American chemical engineer and the Chevron Professor of Chemical Engineering and Mechanical Engineering at the California Institute of Technology. He is a fluid mechanician and creator of the Stokesian dynamics method for simulating suspensions of spheres and ellipsoids in low Reynolds number flows. He is an elected fellow of the American Physical Society, a fellow of the Society of Rheology, as well as a member of the National Academy of Sciences, the National Academy of Engineering, and the American Academy of Arts and Sciences.