 The specific epithet ("tenuiramis") is from the Latin "tenui-" meaning "slender" or "thin" and "ramus" meaning "branch".This eucalypt is reported as being an older form of its sister species, "E. risdonii".Silver peppermint grows in open forest, often in pure stands, on lowlands and hills in south-eastern Tasmania especially in the Derwent River valley, but also on the Freycinet Peninsula and on Flinders Island.