A number of train services have been cancelled because of flooding, the National Rail website said. A landslip in the Stirling area means buses are replacing trains between Bridge of Orchy and Crianlarich.
On the roads, rivers are being reminded to take care in "challenging" conditions as heavy rain continues to hit the country.
Meanwhile, flood alerts have been issued for coastal areas still recovering from severe weekend storms. Heavy rain and strong winds are also expected to hit central Scotland over the next few days.
Tayside and Fife are the worst hit areas today, with many road closures.
The Met Office has amber "be prepared" weather warnings in place for central Scotland while yellow "be aware" warnings cover much of the rest of the country. Snow could fall in the highest areas, forecasters added.
Strathclyde Police issued a warning to drivers on Thurday about the dangers of speeding during adverse weather.
The force said officers stopped two drivers on the westbound M8 between junctions 13 and 16. The men were driving at speeds of 98mph and more than 100mph in a 50mph zone.
Firefighters spent much of the night clearing water away from properties across Fife and Tayside, with a number of people having to be rescued from their cars.
Police said there are a few minor roads closed in central Scotland and Grampian and one in Dumfries and Galloway.
The Met Office has amber "be prepared" weather warnings in place in Tayside, Fife and central Scotland, while yellow "be aware" warnings cover much of the rest of the country.
There are 24 flood warnings in place around central Scotland, Tayside and the Borders while coastal communities, which were hit by severe storms last weekend, have also been put on alert for rising river levels and high waves.
Richard Brown, head of hydrology at the Scottish Environment Protection Agency (Sepa), said: "The heaviest rainfall is expected to be in Stirlingshire, Perthshire, Angus, south Aberdeenshire, Central, the Southern Uplands and an area just to the north of Glasgow. The rain will be accompanied by strong to gale force south-easterly winds.
"There is also a coastal flood risk throughout Friday for the northern, Moray and eastern coastlines including Stonehaven and Orkney. Disruption is possible in areas where defences were damaged over last weekend.
"The rain is expected to gradually decrease during Friday before further rain extends northwards during Saturday."
Last weekend, gale force winds and high tides forced the evacuation of dozens of people from their homes and caused millions of pounds of damage in the east of the country.
Ports and flood defences were damaged in Aberdeenshire and Berwick in what Environment Minister Paul Wheelhouse described as a "perfect storm" of low pressure, high tides and gales.
Mr Wheelhouse said: "With this latest bout of severe weather in parts of Scotland I would reiterate Sepa's advice that the public should remain vigilant and pay attention to Floodline.
"The Scottish Government's Resilience Team is monitoring the situation and is engaged with local responders to understand the impacts of the weather on areas affected and support their efforts to protect communities across Scotland."
Nick Grahame, chief forecaster at the Met Office, said: "We have issued a number of severe weather warnings and it's important people are weather aware by staying up to date with these during this period of unsettled weather.
"Amber means you need to be prepared for the weather and take steps to change your plans and protect you and your family or community from the impacts of the severe weather based on the forecast from the Met Office.
"We'd advise people in the areas affected to expect some disruption and take precautions if they are in an area at risk from heavy rain and flooding."