First named by Edwin Newton in 1888 as a new species of Scaphognathus, Parapsicephalus purdoni was known from just a single partial skull for over a century. The genus Parapsicephalus was named in 1919 by Gustav von Arthaber, pointing out that it was not especially similar to the Upper Jurassic genus Scaphognathus. Several authors in the 20th and 21st century sunk Parapsicephalus into the contemporaneous genus Dorygnathus, as D. purdoni. The skull was recovered from the Lower Jurassic Alum Shale Member of the Whitby Mudstone Formation in Yorkshire, northern England. A skull from the Lower Jurassic Epsilon Shale of Germany was preliminarily described in 2017 by Michael O’Sullivan and David Martill as a second specimen of Parapsicephalus, and demonstrates that it is a distinct genus from Dorygnathus. This second skull is privately owned, but will be donated to a British museum upon the owner’s death.
Both skulls are similar in size, with more complete German skull being 16.5 cm (6.5 inches) long, and the incomplete English skull missing the rostrum and oral margin, being an estimated 20 cm (8 inches) long when it was complete. Both skulls are long and narrow, with the skull roof being gently convex, a feature otherwise seen only in puffin-skulled dimorphodontids among pterosaurs. The eye socket is large, and shaped like inverted triangle with rounded edges. The nostril is a long slit, high on the snout, almost entirely above the antorbital fenestra. The rostrum, only preserved in the German example, shows an unexpected upward curvature of the upper margin and tooth row.
Neither skull preserves any teeth, with the English skull’s lower margin eroded away. The oral margin of the German skull is present, and shows that it had eight pairs of teeth in its upper jaws with roots showing they were splayed, like many rhamphorhynchids.
The convex upper margin of the skull has helped link Parapsicephalus to Dimorphodon by several authors, including those performing phylogenetic analyses. The German skull has shown that this is an unlikely relationship, with the low number of splayed teeth being characteristic of rhamphorhynchids. Nothing is known from the rest of the skeleton, but like other rhamphorhynchids, Parapsicephalus likely had narrow wings and a long tail with a vertical vane at its tip. Based on comparison to relatives, Parapsicephalus probably had a wingspan of about 1.8 m (6 feet).
When Parapsicephalus lived, about 180 million years ago, much of Europe was covered in low subtropical islands and lagoons, on the northern shore of the ancient Tethys Ocean. Like most rhamphorhynchids, Parapsicephalus probably fished on the wing.