Work at Sutton North bridge is expected to take until July
The cost of rebuilding North Yorkshire's flood-damaged roads and bridges is expected to top £3m.
Roads, bridges and property in areas around Helmsley and Thirsk were the worst affected by flash floods which swept through the county on 19 June.
The Sutton-under-Whitestonecliffe to Thirlby road needs to be completely rebuilt, contractors have said, as does the village's Sutton North bridge.
North Yorkshire County Council said the work would take until mid-July.
Some of the county's most remote villages were completely cut off after a month's rain fell in just a few hours.
Although priority routes have reopened, council contractors are continuing to work in Hawnby, Sutton-under-Whitestonecliffe and Thirlby.
A temporary structure has been put in place over Chapel Bridge, Hawnby, after it was partially swept away.
Mike Moore, director of environmental services, said: "Engineers across the area are completing a detailed assessment of precisely what work needs to be done. That work will be carried out over the coming weeks and months.
"Our target is to get things back to normal as quickly as possible for the many small communities across the area that were affected by the flood damage."