The name refers to the distinctive anvil-shaped first dorsal fin and spine displayed by mature males of the genus.

[8] The crest may have played a role in mating rituals, aided in clamping to the belly of larger marine animals, or been used to frighten potential predators.

[9] Like other members of Stethacanthidae, Stethacanthus had unique pelvic girdles, single-crowned and non-growing scales, a pectoral fin composed of metapterygium with an accompanying ‘whip’ attached and a distinctive first dorsal fin and spine, termed the spine-brush complex.

In addition to these features, Stethacanthus also had male pelvic claspers with non-prismatic calcified cartilage at the distal ends.

The spines resemble those of modern sharks and rays but curiously lack any enamel-like surface tissue.

The so-called "brush" is not fibrous as was originally believed, but consists of a number of parallel, membranous tubules[6] made of globular calcified cartilage.

[13] In Stethacanthus, the pelvic girdles consist of sheets of prismatic cartilage, each in the shape of a subtriangular, rounded plate.

This feature, accompanied with a broadening of the pelvic girdle in order to accommodate the increased number of radials is a characteristic of Stethacanthus and other symmorriids.

[14] The males had claspers that were club-shaped at the distal ends and composed of non-prismatic globular calcified cartilage.

[11] Since complete skeletons were extremely rare, Stethacanthus classification was vague and based on few characteristics.

It was not until 1974 that the family Stethacanthidae was defined by Richard Lund because Stethacanthus differed so greatly from other elasmobranchs of the time.

If this were the case, primitive chondrichthyans would have appeared with shark-like scales based instead on globular calcified cartilage.

Another feature of note is the thin, acellular bone layer coating the brush and baseplate of the spine-brush complex.

[12][13] Taxonomic relationships are hard to define for Stethacanthus as there is much variability in the characteristics of the discovered specimens.

[14] Chondrichthyes is a monophyletic group characterized by the development of endoskeletal tesserae (mineralized blocks of cartilage) and internal fertilization.

[10] More recently, Symmoriiformes as a whole has been reclassified as part of Holocephali, meaning that Stethacanthus may have been more closely related to modern chimaeras than to sharks.