A number of major routes have been hit by the severe weather, including the M876 northbound at junction two and one lane of the M80 heading north.
Yellow weather warnings for rain and wind are in place across much of the country through until Saturday.
Wet conditions have also led to the postponement of a match between St Mirren and Hearts at the Simple Digital Arena in the town on Friday.
High winds saw the Forth Road Bridge closed to double-decker buses, motorcycles, cyclists and pedestrians.
The Scottish Environmental Protection Agency (Sepa) issued flood warnings and alerts for most of the country on Thursday, lasting for two days.
Sepa said: "Prolonged periods of rain are expected over the next 48 hours across western and central Scotland.
"This may result in localised flooding and surface water impacting communities across these areas."
A yellow "be aware" warning for snow and ice has also been issued by the Met Office for north and central Scotland on Saturday.
ScotRail announced trains in the Central Belt, The Highlands and Lothian and The Borders have been affected by the flooding.
Bus replacement services have been arranged to assist passengers with their travels.
The Central Belt
-Delays to services between Edinburgh and Glasgow Queen Street via Falkirk High
-Cancellations to services between Glasgow Queen Street and Aberdeen
-Cancellations to services between Glasgow Queen Street and Alloa
-Cancellations to services between Glasgow Queen Street and Dunblane
-Cancellations to services between Edinburgh and Dunblane
For more updates click hereREAD MORE: Scotland's weather: Four yellow weather warnings issued for 75mph gales, snow and heavy rainThe Highlands
- Alterations to services between Glasgow Queen Street and Inverness
- Alterations to services between Edinburgh and Inverness
For more updates click hereLothian and The Borders
-Cancellations to services between Edinburgh and Bathgate
-Services between Edinburgh and Bathgate are subject to delays due to the heavy rain.
For updates on train journeys visit the ScotRail website hereRoads
Roads have also had to close due to the heavy downpour.
A section of the A737 at Linwood Toll in Paisley is flooded, with an ambulance running into difficulty and getting stuck in the floods.
Part of the M876 has had to close at J2 due to flooding and traffic is being diverted via slip roads off the motorway.