The holotype of Elfridia is a left mandible. Several other tooth-bearing fragments and isolated postcranial elements are assigned to this taxon. It is diagnosed by having lingually recurved tips of the teeth that are positioned asymmetrically on the labial portion. There are nine to ten teeth on the mandible with a greatly enlarged tooth along the mid-length of the tooth row.
Relationships
Thayer placed Elridia within the Gymnarthridae, but the fragmentary nature of the material has precluded its incorporation into a phylogenetic analysis to more thoroughly test and to evaluate its relationships with other 'microsaurs.' He compared it to both Euryodus and Cardiocephalus, noting a mixture of features shared between the two gymnarthrids, such as the enlarged tooth and striations on the teeth.