Eysyslopterus is a genus of eurypterid, an extinct group of aquatic arthropods. Eysyslopterus is classified as part of the family Adelophthalmidae, the only clade within the derived ("advanced") Adelophthalmoidea superfamily of eurypterids. One fossil of the single and type species, E. patteni, has been discovered in deposits of the Late Silurian period (Ludlow epoch) in Saaremaa, Estonia. The genus is named after Eysysla, the Viking name for Saaremaa, and opterus, a traditional suffix for the eurypterid genera, meaning "wing". The species name honors William Patten, an American biologist and zoologist who discovered the only known fossil of Eysyslopterus.