The Cassini spacecraft ’ s Grand Finale orbits provided a unique opportunity to probe Saturn ’ s gravity field and interior structure . Doppler measurements \citep Iess2019 yielded unexpectedly large values for the gravity harmonics J _ { 6 } , J _ { 8 } , and J _ { 10 } that can not be matched with planetary interior models that assume uniform rotation . Instead we present a suite of models that assume the planet ’ s interior rotates on cylinders , which allows us to match all the observed even gravity harmonics . For every interior model , the gravity field is calculated self-consistently with high precision using the Concentric Maclaurin Spheroid ( CMS ) method . We present an acceleration technique for this method , which drastically reduces the computational cost , allows us to efficiently optimize model parameters , map out allowed parameter regions with Monte Carlo sampling , and increases the precision of the calculated J _ { 2 n } gravity harmonics to match the error bars of the observations , which would be difficult without acceleration . Based on our models , Saturn is predicted to have a dense central core of \sim 15–18 Earth masses and an additional 1.5–5 Earth masses of heavy elements in the envelope . Finally , we vary the rotation period in the planet ’ s deep interior and determine the resulting oblateness , which we compare with the value from radio occultation measurements by the Voyager spacecraft . We predict a rotation period of 10:33:34 h \pm 55s , which is in agreement with recent estimates derived from ring seismology .