Fossil record of anapsids: Abbreviations: Jur, Jurassic; Pen, Pennsylvanian; Per, Permian; Tri, Triassic. You can click on the names or stratigraphic ranges of the anapsid taxa in the image above.
Anapsid diversity appears to have reached its peak in the Upper Permian (about 260 million years ago), at which time lanthanosuchids, millerettids, nyctiphruretians, pareiasaurs, and the first procolophonoids constituted a large proportion of the terrestrial vertebrate fauna of South Africa and Russia.
Apparently, only procolophonoids survived the large extinction event at the end of the Permian, and a large evolutionary radiation of that group took place in the Triassic. However, procolophonids also became extinct by the end of the Triassic (about 210 million years ago), at which time turtles were the only remaining anapsids. The oldest known turtles (Proganochelys) date from the Upper Triassic, at which times they had already lost their marginal teeth (although they retained the palatal denticles characteristic of early amniotes) and acquired the shell and plastron. The oldest known crown-turtles (members of Chelonia) only date from the Jurassic period (the cryptodire Kayentachelys).
Laurin M. and R. R. Reisz. 1995. A reevaluation of early amniote phylogeny. Zoological Journal of the Linnean Society 113: 165-223.
Lee, M. S. Y. In press. A taxonomic revision of pareiasaurian reptiles: implications for Permian terrestrial palaeocology. Modern Geology 66 pages, 17 figures.
Milner, A. R. 1993. Amphibian-grade Tetrapoda. In: M. J. Benton (ed.) The Fossil Record: 665-679. London: Chapman & Hall.