Solastella cookei was named by Stocker and Kirk (2016). Its type specimen is TMM 41672-246, a partial skull (partial skull and articulated left mandibular ramus missing anterior portion of the premaxilla, right maxilla, right circumorbital elements, and right side of t), and it is a 3D body fossil. Its type locality is Purple Bench, which is in an Uintan terrestrial horizon in the Devil's Graveyard Formation of Texas. It is the type species of Solastella.