Hystricurus flectimembrus was named by Ross (1951) [Paratypes: YPM 17970-1, 17973-9, 18300]. Its type specimen is YPM 17972, a cephalon/head (cranidium), and it is a 3D body fossil. Its type locality is Locality 6, Hillyard's Canyon, Zone "F", which is in a Stairsian shallow subtidal horizon in the Garden City Formation of Idaho. It is the type species of Flectihystricurus.

It was recombined as Flectihystricurus flectimembrus by Adrain et al. (2003).