OBSERVATIONS of Antarctic super tabular icebergs1–5, which can exceed 100 km on a side, have shown that their origin can frequently be traced to previously existing super ice tongues, which are a class of massive seawards-extending ice shelves. Furthermore, a history of cyclic growth and calving can often be inferred2–4 or demonstrated6,7. Because the calvings do not generally occur along a line coincident with the grounding line, where, under normal tidal flexure the stresses are greatest8,9, and because multiple fracturing is observed1,2 we have sought a nontidal theory for ice-tongue fracture9. A mechanism for generating significant bending stresses at locations along an ice tongue far from the grounding zone is by vibration of the glacier in a mode higher than the fundamental10. In this report, we outline an approximate analysis of the modes of free vibration of a buoyant, elastic, tapering ice tongue floating in shallow water of variable depth.