Radio frequency (RF) shields used with magnetic resonance imaging (MRI) apparatus may experience gradient field induced eddy currents and RF field induced eddy currents. These eddy currents can cause the RF shield to heat up at an undesirable rate. RF shields are designed to have a desired degree of RF shielding and a desired heating attribute. Design goals for RF shields include gradient field transparency and RF field opacity, both of which can be influenced by eddy currents. Example methods identify a gradient field that will induce eddy currents and identify an RF field that will induce eddy currents. If a region on the RF shield is identified where the desired heating attribute will not be achieved, then a pattern of axial cuts and azimuthal cuts can be made in the RF shield to reduce gradient eddy current heating in the RF shield while maintaining desired RF shielding.