In this paper the densification of ceramics under flash sintering is modelled using an approach based on the heat equation coupled with a apparent activation energy kinetic equation for densification, leading to a system of nonlinear differential equations. Methods to analyse the system either by numerical solutions or via bifurcation theory are presented. Measurements needed to estimate sintering kinetic parameters are executed. The model shown explains the two main features of flash sintering: A characteristic electrical field threshold independent on the temperature, and an incubation time to flash sintering. The results are in agreement with experimental results obtained for Yttria Stabilzed Zirconia and for nanosized BaTiO3. It confirms that the critical condition for the Flash phenomenon is rather the temperature dependent resistivity than the sintering kinetics.