Firefighters were alerted to the incident at Stirling County Rugby Club just before 8.45pm on Monday.
A spokeswoman said the Stirling fire station water rescue team sent a boat to rescue 14 members of the public from the club due to the flood waters.
Everybody was said to be "fit and well" following the rescue.
In a flooding update, Stirling Council tweeted that Wallace High, Ochil House and Castleview Primary would be closed on Tuesday.
Some local road closures also remained.
In Edinburgh on Monday, torrential rain led to severe flooding, bringing long delays to many travel routes in the west of the capital.
There were several road closures and tram services were suspended.
Currie Library and Sighthill Library were closed due to the weather, with rainwater reported to be leaking into the buildings, although they were expected to reopen on Tuesday.
Tuesday brought an improved picture, although some disruption to bus routes remained in the Bankhead area of Edinburgh in the morning.
On Monday, Liberal Democrat MP Christine Jardine posted a video on Twitter from inside her constituency office on St John's Road in Corstorphine as water crashed against the front window.
In the same area, footage posted on social media showed one man had resorted to sitting on the roof of his car with the vehicle unable to move through the flooded street.
At a Farmfoods in Leven, Fife, a Facebook video showed rain pouring into the store from the ceiling.
Darryl Wright, 34, who filmed the footage, told the Press Association: "We suddenly heard this noise as if someone turned on a loud shower, we turned around and the rain was just pouring in from the ceiling."