A model for describing plasma decay in field reversed configurations has been developed. The model is based on simple resistive MHD equations in which thermal conductivity and radiation losses as well as inertial effects in the momentum balance equation are neglected. With these assumptions, it is shown that Ohmic dissipation is balanced by plasma flow in such a way that the initially uniform profile is maintained uniform and that the functional dependence of the pressure on the poloidal magnetic flux is also maintained (this dependence defines a family of equilibria). This result is independent of the magnitude or profile of the conductivity. It is therefore possible to describe the time evolution of the system as a continuous sequence of equilibria which pertain to the same family and satisfy proper boundary conditions. The method is applied to the Hill's vortex model and all decay times of interest as well as the time evolution of the separatrix are found. The existence of bifurcation points in the parameter space of the equilibria may account for the different behaviour of discharges with 5 mtorr and 20 mtorr deuterium filling pressure observed in the FRX-C experiment at Los Alamos.