Euptychognathus (lit. 'well-folded jaw') is a genus of lystrosaurid dicynodont, an extinct type of therapsid (a group that modern mammals also belong to). The type species E. bathyrhynchus was first named in 1942 as a species of Dicynodon, D. bathyrhynchus, but was not recognised as being its own genus until 2011. Although relatively rare, fossils of Euptychognathus have been discovered in multiple different formations across several countries, including the Usili Formation in Tanzania, the Madumabisa Mudstone Formation of Zambia, and the Balfour Formation of the Karoo Basin in South Africa.

Two species of Euptychognathus are recognised, the type species E. bathyrhynchus and E. kingae. Both are very similar anatomically and largely differ in skull proportions—E. bathyrhynchus has a taller, narrower skull, while E. kingae has a shallower but much wider head. Euptychognathus is a member of the family Lystrosauridae and closely related to the well-known Lystrosaurus and shares some of its distinctive traits, particularly the deflected shape of the snout. Euptychognathus was one of the first lystrosaurids to be definitively recognised from the Permian, and demonstrates that the unusual morphology associated with Lystrosaurus evolved before the ecological disruptions of the Permian-Triassic mass extinction. The widespread range of Euptychognathus despite its relative rarity is unusual for a Permian dicynodont, as many species appear to be locally endemic to individual and immediately adjacent basins.

Although typically recognised as lystrosaurid, the precise relationships of Euptychognathus have not been settled in phylogenetic analyses over the years, including some that placed it outside of Lystrosauridae altogether. The discovery of more specimens of Euptychognathus as well as other Permian lystrosaurids (Madumabisa, Lystrosauravus) have helped to resolve the interrelationships and evolution of lystrosaurids, which re-affirm the inclusion of Euptychognathus in the group.

While the genus Euptychognathus was not named until 2011, fossils of Euptychognathus have been known since the middle of the 20th century. In 1942, German palaeontologist Friedrich von Huene named a new species of Dicynodon, Dicynodon bathyrhynchus, from a single skull (GPIT-PV-117020) discovered in what is now recognised as the Usili Formation in Tanzania. The skull was discovered Ernst Nowack on an expedition to the Usili Formation with his wife Maria Nowack between 1934 and 1936, who sent the skull to Germany to be examined. Von Huene named the new species for its distinctively deep snout, which resembles that of another dicynodont, Lystrosaurus. At the time, the genus Dicynodon acted as a taxonomic wastebasket that many species of Permian dicynodonts were dumped into, often over-split into an excessive number of species.

The validity of D. bathyrhynchus was contested during subsequent attempts to revise the taxonomy of Dicynodon, with some authors considering it a valid species (e.g. Sidney H. Haughton and Adrian Smuts Brink in 1954, Gillian King in 1988) while others synonymised it with Dicynodon lacerticeps (e.g. Brink in 1986). One of the major issues affecting the matter is that the skull has been heavily reconstructed with plaster, with a particularly large section of skull below the naris (nostril opening) being entirely reconstructed and putting its proportions into question.

In 2011, palaeontologists Christian F. Kammerer, Kenneth D. Angielczyk and Jörg Fröbisch thoroughly revised the taxonomy of Dicynodon, including the status of D. bathyrhynchus. The species was almost declared to be invalid until they recognised two additional skulls matching the holotype specimen in the collections of the Council for Geoscience (CGP) in Pretoria, South Africa (CGP AF107-83 and CGP/1/310), as well as a third skull in the collections of the University of California, Berkeley (UCMP 42714). These three skulls are better preserved and more complete, and confirm the unusual and distinctive proportions of the holotype specimen GPIT-PV-117020. From their revised taxonomy, it was clear that this species did not belong to the genus Dicynodon.

Without any existing available names for this species, Kammerer and colleagues named the new genus Euptychognathus with the new combination Euptychognathus bathyrhynchus as the type species. The name means lit. 'well-folded jaw' and combines the Ancient Greek words ευ ("good, well"), "πτυχoς" (translated as "folded"), and γνάθος ("jaw"). The name is a literal description of the distinct downwardly deflected snout, but also alludes to the name Ptychognathus—the original name given to Lystrosaurus by Richard Owen in 1860, but already preoccupied by a genus of freshwater crab.

While the original holotype specimen was discovered in Tanzania, these three additional specimens all come from the Karoo Basin in South Africa. Several more specimens have also been discovered and recognised since 2011, including five more from South Africa (RC 401, RC 464, RC 533, RC 798 and SAM-PK-K11781), another from Tanzania (NMT RB1213), one from the Luangwa Valley in Zambia (NHMUK PV R 37079) and one from the Zambezi River Valley of uncertain province, either hailing from either Zambia or Zimbabwe (NHMUK PV R 36715). The majority consist only of skulls and lower jaws, and only SAM-PK-K11781 from South Africa preserves any of the postcranial skeleton—a series of nine partial vertebrae and part of a single rib.