While several current Flood models posit an Upper Cenozoic Flood/Post-Flood Boundary, none of them adequately address the serious problem that they engender regarding biblical kinds and their relationship to the Genesis narrative. Genesis 7 lays a constraint on the development of Flood models— only one pair of every terrestrial unclean kind was taken into the Ark. One recent Flood model places the boundary between the Neogene and Quaternary. This puts multiple genera within a terrestrial unclean kind on both sides of the boundary, contravening the traditional understanding of the biblical kind. This paper lays out the issue and examines possible alternative solutions, but concludes that the Neogene-Quaternary boundary is not viable within a biblical framework.