In this paper, a 1D numerical, time-dynamic, fluid model (SHEATHSIM) has been developed to study the effect of RF chuck bias on high density electronegative discharges especially under conditions of sheath inversion and negative ion extraction. In each sheath, ion momentum conservation and ion continuity equations, closed by Poisson's equation, are solved for a given set of bulk densities, temperatures and mean free path lengths of each ionic species. Two such sheaths are closed by a common bulk potential and current continuity. Qualitatively, high electronegativities (≥100), low electron temperatures (≤2.5 eV), high asymmetries (≥10), DC coupling of bias power and low frequencies (≈100 kHz) tend to favour sheath inversion and subsequent negative ion extraction. Quiescent floating sheath simulations show the self-consistent rise of the plasma regions and the Bohm criterion. Such modelling in conjunction with source antennae electromagnetics and chemical kinetics can lead to computer aided process and reactor design with a view to reducing charge-up damage through negative ion extraction.