The parties, who run Stirling Council in coalition, said they were standing up for "symbols the men and women of Stirling have fought and died under for 300 years".
They added that it was a bid to form part of the debate over next year's independence referendum and would reflect the diversity of views in the area.
However, the move has been criticised by opposition leaders, coming at a time of tens of millions of pounds worth of cuts and industrial action at the council, and by academics, who have said it is a turn-off for voters.
Tonight's motion before the council refers to "symbols that the men and women of Stirling have fought and died under for 300 years".
Signed by Labour's Danny Gibson and Tory counterpart Callum Campbell, a one-time parliamentary candidate for the party, it adds: "Council resolves to stand up for the symbols of our country by flying the Union flag from the main pole above the council building and the council flag from the freestanding flagpost in the ground of Old Viewforth."
The councillors behind the motion said the promotion of the Union flag as the main symbol above Stirling's headquarters, alongside a Saltire, would bring it into line with the Scottish Parliament.
However, Dr Michael Rosie, a senior lecturer in sociology specialising in issues around national identity at Edinburgh University, said: "This motion is slightly odd largely because there's no evidence that anyone is getting that excited about flags.
"The mainstream No campaign has avoided issues around identity. Seeking electoral advantage through notions of Britishness is a political dead end and I imagine things like this motion will turn so many No voters off.
"References to having 'fought and died for 300 years' is also a cheap shot and ill advised."
Dr Neil McGarvey, an expert in Scottish Politics and local government at Strathclyde University, added: "This seems like a highly party politicised act on the part of the council and brings to mind the type of identity politics of Northern Ireland constructed around issues such as flags, names and symbols."
Most councils have around 20 designated days-a-year when the Union flag is flown, mainly Royal birthdays, anniversaries, visits and other special events.
Labour-run Glasgow City Council has been picketed by fringe Loyalist groups for months over flying the Saltire, even rebuffing offers from them for a new flagpole for both to be flown.
Stirling Council SNP group leader Graham Houston said: "We're having to save £24 million and we're going through a labour dispute with bins on the streets unemptied and the administration wants to debate flags.
"I'm more than happy to discuss the referendum but to use their majority to fly a flag as part of their No campaign is a ridiculous position to take."
Last night, Cllr Campbell said there had been "online hysteria" over the motion, insisting the flags element was only part of it.
He also said it had been generated by "hotheads" keen to avoid a debate on the referendum and the flags policy of other Governmental buildings.
He added: "I'm not exactly sure what the council's policy is on flying the Union flag. It flies sometimes. But I see no reason why we shouldn't be the same as Holyrood."