A lapping control system for a row of thin film magnetic transducers formed on a substrate. Each of the magnetic transducers comprises a magnetoresistive (MR) element, and the row is supported on a holder which has an elongated H-shaped slot near one edge to form a beam member upon which the row is mounted. The beam member is capable of being deflected in a substantially quadratic curvature when subjected to pressure from a pressure transducer at the middle of the beam member. The resistance of each of the MR elements is measured during lapping, and a control signal is generated to control the pressure transducers to control lapping with proper BALANCE and BOW and to terminate lapping when the desired MR element height is reached.