Skeletal remains of Tristychius arcuatus commonly occur in ironstone nodules from the Scottish Upper and Lower Oil Shale Groups. This material is clearly distinguishable from the small shark from Glencartholm described by Traquair, Woodward and Moy-Thomas under this name. Study of the latter shows that its finspines are distinctly different from the holotype of T. arcuatus and, therefore, it has been renamed.

Tristychius arcuatus sensu stricto is a medium-sized hybodont shark with a short gape, a functionally heterocercal tail and narrow-based, tribasal pectoral fins. Its most unusual feature is a well developed opercular gill cover composed of long hyoid rays. Evidence suggests that this character was present in several Palaeozoic sharks, although it is absent in all Recent elasmobranchs. It is not clear whether it was primitively present in chondrichthyans or evolved separately in several lineages.

Hybodonts and ctenacanths are recognised as separate, specialised shark radiations, neither of which can be directly ancestral to Recent sharks. Of the two, hybodonts appear to be more closely related to Recent forms, although the presence of typical hybodont finspines in Tristychius arcuatus indicates that they had diverged from ancestral euselachians before the beginning of the Carboniferous.