Leptocleidus clemai was named by Cruickshank and Long (1997). Its type specimen is WAM 92.8.1-1 to 68, a partial skeleton (right femur, , psrt of tibia, psrts of the left femur, possibel fragments of lower jaw, lacking teeth, pelvic girdle element, part of a propodial head, part of ), and it is a 3D body fossil. Its type locality is "Stone Wall," Murchison House Station, which is in a Barremian/Aptian fluvial sandstone in the Murderong Shale Formation of Australia.