This paper presented an analytical SS model to determine the subthreshold swing (SS) of an elliptic junctionless Gate- All-Around (GAA) FET using ferroelectric. Analyzing a GAA FET with an elliptic cross-section was essential because it is difficult to manufacture a perfectly circular GAA FET. The results of the proposed SS model agreed well with 2D numerical simulation. Using this analytical SS model, SS was analyzed for the eccentricity and the ratio (Pr/Ec) of permanent polarization Pr and coercive electric field Ec in an elliptic junctionless GAA FET with an MFMIS (Metal-Ferroelectric-Metal-Isulator- Semiconductor) structure using ferroelectric. As a result, the changing rate of the average surface potential due to the gate voltage increased and SS decreased as the eccentricity increased. It was found that the inner gate voltage amplified more than the outer gate voltage due to the ferroelectricity, better controlling the carriers in the channel, thereby reducing SS. As the Pr/Ec decreased, the changing rate of the ferroelectric charge for the outer gate voltage increased and SS decreased. As the eccentricity increased, the changing rate of SS for Pr/Ec decreased. There was no significant change in SS until the eccentricity was about 0.5. The SS began to decline above 0.5 due to the changes in ferroelectric charge, inner gate voltage, and average surface potential for the outer gate voltage.