The E39 between Stavanger and Randaberg runs 5.9 kilometres under the Byfjord in Rogaland. The tunnel opened in 1992 and is the main part of Rennfast, the fixed link to Rennesøy.

At its opening, the Byfjord tunnel was Europe's longest and the world's deepest undersea road tunnel, with its deepest point 223 metres below sea level. The ramp on the Stavanger side is unusual: it was built as an excavated and sunken structure on piles, not blasted from rock.

The tunnel is part of the link that gave Stavanger a ferry-free road to Rennesøy, and together with the Mastrafjord tunnel it tied the whole municipality of Rennesøy to the mainland.