Eryopiformes was named by the German paleontologist Rainer R. Schoch in 2013.

He defined it as a node-based taxon to include Eryopidae and Stereospondylomorpha.

Unlike previous analyses, a phylogenetic analysis he performed found no support for a monophyletic Euskelia, that is defined to include Dissorophoidea and Eryopidae (and also usually includes Zatracheidae), in relation to Stereospondylomorpha.

In this analysis, Eryopidae and Stereospondylomorpha usually formed a monophyletic clade that excludes the clade formed by Zatracheidae and Dissorophoidea.

Thus, he named this newly identified group as Eryopiformes.