Mt Tungnafell (1,392 m) is a convex and steep mountain in the northern slopes of the massif, upon which the glacier rests and takes its name from.  The glacier is about 10 km long, 5-6 km wide and has an area of 50 kmē.  The mountain massif is rather steep all around and indented with gullies and gorges to the south and west.  Its highest point, Hahyrna (1,520 m), protrudes from the western edge.

This mountain massive is  old and eroded and created by sub-glacial eruptions with a SW-NE fissure system.  Its caldera is about 10 km long, 4 km wide and 200 m deep.  Holocene lava fields are situated just north of the glacier as well as the craters Bokki and Dvergar.  In the Vonarskard Pass, southeast of the glacier, traces of a still older caldera, decorated with the rhyolite mountain Skrauti and the basaltic hyaloclastite mountain Deilir.