“Huge amounts of water” started rushing down the hillside with reports of water 5ft (1.5m) deep flooding some homes.
Main Road in Gwaelod-y-Garth and Heol Goch between Gwaelod-y-Garth and Pentyrch had to be closed for clean-up operations.
Highways and cleaning staff have been working on-site to clear the roads and remove debris, said Cardiff council.
However, significant damage has been caused to roads, it said, with mud, silt, debris and other obstructions.
Overnight accommodation was arranged for one family on Thursday, with support also provided to a second family on Friday, it added.