Teyumbaita sulcognathus is a peculiar endemic Brazilian rhynchosaur that remained somewhat obscure until recently, when its skull anatomy was described and a new generic name was assigned to this highly autapomorphic taxon. Here, the postcranial skeleton of Teyumbaita sulcognathus is for the first time fully described based on the holotype and the two more complete referred specimens. Rhynchosaur postcranial anatomy has usually been considered to be rather conservative, but T. sulcognathus shows unforeseen morphological variation. Autapomorphic traits were added to the diagnosis of T. sulcognathus and intraspecific variation was also identified. In addition, six new phylogeneticaly informative postcranial characters were recognized. Some of these represent apomorphies of clades such as Rhynchosauridae (axis with ventral keel, crest on the anteromedial surface of tibial shaft) and Hyperodapedontinae (postaxial cervical vertebrae with ventral keel, supinator process composed of a low supinator ridge and the ligament groove), revealing new support for their monophyly. The rhynchosaur diversity of the Otter Sandstone Formation (England) was also evaluated based on a phylogenetic analysis. The results suggest that the postcranium EXEMS 79/1992 is more likely related to Fodonyx spenceri than to Bentonyx sidensis.