The main source of the Axe River is in the shallow valley between Mt Burfell and  Pass Leggjarbrjotur. It meanders thought the Axe River Valley, across the Bishops’ Lava Field, where it has deposited sand and gravel during the millennia and changed its course a few times. According to Sturlunga Saga it was diverted to run over the brink of the Almannagja fault to bring fresh water supplies closer to the assembly area of the ancient parliament.

The present concrete bridge by the Drowning Pool was built in connection with the festivities and celebrations of the millennium of the parliament in 1930. The river has an average flow of 3-4 m³/sec., but sometimes swells during spring and early summer, when the winter snow melts. Geese breed on the small islands and harlequin ducks are frequently seen on the water.