Spongia infundibuliformis Linnaeus, 1759: 1348; Esper, 1791-1794: pl. XI (Spongia infundibuliformis).
Isodictya infundibuliformis : Bowerbank, 1866: 317; 1874: 137, pl. LIV(Isodictya infundibuliformis); Norman, 1869: 298; Schmidt, 1874: 430; Fristedt, 1885: 45, pl. III fig. 10.
Tragosia infundibuliformis : Gray, 1867: 513; Arnesen, 1903: 24; Stephens, 1912: 38; Arndt, 1913: 114; Stephens, 1917: 13; 1920: 66; Burton, 1930a: 494; Arndt, 1935: 90, fig. 192; Lévi, 1950b: 12; Burton, 1957: 30; Descatoire, 1969a: 188.
Reniera palescens n.sp. Hansen, 1885 (fide Burton, 1930a)
Thrinacophora microdragma n.sp. Von Lendenfeld, 1897: 84, fig. 3.
?Axinella calyciformis : Burton, 1957: 31
Axinella infundibuliformis : Burton, 1959a: 48; Burdon-Jones and Tambs-Lyche, 1960: Table I; Borojevic et al., 1968: 11; Descatoire, 1969a: 188; Könnecker, 1973: 456; Hiscock et al., 1983(1984): 22, pl. 2e; Ackers et al., 1985: 91, fig. 15; 1992: 83, photo 187; Bamber and Coughlan, 1989.
Arndt, 1935 mentions further synonyms without quoting sources:
Spongia crateriformis
Spongia calyciformis
Spongia pocillum
Phakellia infundibuliformis
Halichondria infundibuliformis
Placochalina infundibuliformis
Cribrochalina calyciformis