Employing our current understanding of the structure and dynamics of Saturn's magnetosphere, we present a time-dependent model of the kronian Dungey cycle magnetotail, which is based upon a modification of a similar model developed for Earth's magnetotail (Milan, 2004a). The major difference arises due to the rapid rotation of Saturn and the partial corotation that this imposes on the open field lines threading the polar cap. This results in twisted tail lobes, with the form of concentric cylinders of oldest to newest open flux from the inside out. The oldest, and hence longest, open field lines form the backbone of a highly extended magnetotail. Surrounding this are bundles of field lines disconnected by tail reconnection, propagating down-tail at the solar wind speed. Owing to the twisted nature of the tail, these bundles remain entangled with the lobe cores to form exterior flux ropes. In the limit that the addition and removal of open flux from the magnetosphere by magnetic reconnection can be treated as a last-in-first-out system, we formulate a description of the flux transport within the tail and drive this with estimated dayside reconnection voltages deduced from Cassini observations of the IMF made upstream of Saturn (Jackman et al., 2004).