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A significant percentage of the analysis applied to memristors is based on the Linear Drift Model. In the Linear Drift Model the resistance of the doped region increases in direct proportion to the width of the doped region. It is shown that this is not consistent with the physical conservation of the mobile vacancies. A circuit model is proposed which is consistent with the conservation of the mobile vacancies and takes into account a high constant intrinsic resistivity indicative of the memristor “off state”. A numerical analysis (NA) scheme is tested and compared with reported Hewlett Packard memristor data and with the theoretical solution for the Linear Drift Model.