Up to 30mm could fall within an hour in some places and 60mm within two to three hours , the Met Office said today.
It has issued a yellow - "be aware" - severe weather warning for 9am to 10pm on Friday and 11am to 9pm on Saturday.
The agency said: "There is a small chance that homes and businesses could be flooded quickly, with damage to some buildings from floodwater, lightning strikes, hail or strong winds.
"There is a small chance of fast flowing or deep floodwater causing danger to life.
"Where flooding or lightning strikes occur, there is a chance of delays and some cancellations to train and bus services.
"Spray and sudden flooding could lead to difficult driving conditions and some road closures.
"There is a slight chance that power cuts could occur and other services to some homes and businesses could be lost."
A spokeswoman said scattered heavy showers and thunderstorms were likely to develop on Friday, particularly in the afternoon, which would ease only slowly through the evening.
She said: "Some places will miss the worst of the heavy showers and thunderstorms, but where they do occur they are likely to bring torrential rain with the potential for 20-30mm of rain to fall in an hour and perhaps as much as 50-60mm in three hours in a few locations.
"Lightning and large hail are also possible."
However, she said it was difficult to predict where the heaviest rain would fall.
She said: “Details of exactly where will see the worst impacts from these storms are likely to be uncertain until quite close to the time they break out.”
On Saturday, heavy showers and thunderstorms are expected to develop by late morning across inland Scotland.
The Met Office spokeswoman said: "Some of the storms could be severe, and with generally light winds, will be slow-moving.
"Whilst some areas may escape with a dry day, where storms do develop some torrential downpours are possible.
"There is the potential for 20-30mm of rain to fall in an hour, and as much as 50-70mm in two to three hours.
"As well as heavy rain, frequent lightning and some large hail are also possible."
A Traffic Scotland spokesman said: “The Met Office has issued a yellow warning for rain for most of mainland Scotland from Friday morning through to Friday night. A further yellow warning for rain is in place from Saturday mid-morning until Saturday night, covering much of western and central Scotland.
“The weather may lead to difficult driving conditions, with the possibility of surface water, spray and reduced visibility. As always, motorists should take extra time to plan their journeys, follow police advice and drive to the conditions.
“Drivers can use the Traffic Scotland mobile website – my.trafficscotland.org – to get the latest information on the trunk road network, as well as check the @trafficscotland twitter page for updates.”
Meanwhile, the RAC said one in 20 drivers admitted to getting stuck after driving into floodwater.
It said its survey of more than 2,000 motorists had also found one in five of the vehicles involved had needed repairs.
A total of 7 per cent of them were written off by insurers because they were irretrievably damaged.
The motoring group said water being sucked into the engine was the biggest risk when driving through floods, which it said could cause catastrophic damage.
Spokesman Simon Williams said: “If there’s any element of doubt about whether the water is shallow enough to drive through, the sensible thing to do is to turn around and go another way.
“Sometimes though, the pressure of being ‘on time’ is too great and causes people to take risks they really should not.”