A method and apparatus for finishing a workpiece surface using MR fluid is provided wherein the workpiece is positioned near a carrier surface such that a converging gap is defined between a portion of the workpiece surface and the carrier surface; a magnetic field is applied substantially at said gap; a flow of stiffened MR fluid is introduced into said converging gap such that a work zone is created in the MR fluid to form a sub-aperture transient finishing tool for engaging and causing material removal at the portion of the workpiece surface; and the workpiece or the work zone is moved relative to the other to expose different portions of the workpiece surface to the work zone for predetermined time periods to selectively finish said portions of said workpiece surface to predetermined degrees.