A total of 35 flood warnings and 10 flood alerts were in force by Saturday while the A9 was flooded near Dunkeld.
ScotRail and other services were halted by flooding of the Perth-Inverness rail line, which has been closed south of Dunkeld since Friday.
Emergency speed restrictions were also imposed on the Glasgow-Dumfries route near Sanquhar.
Network Rail Scotland said: “There is flooding at trackside with running water coming from above the line between Stanley and Dunkeld.
“The line is likely to remain closed until water flow off the hill subsides.”
Traffic Scotland reported flooding on the A9 near Dunkeld after a burn burst its banks.
The Met Office issued separate yellow severe weather warnings for rain until 9pm on Friday, and from noon on Saturday until 3am on Sunday.
They cover areas north and south of the Central Belt.
The agency forecast 20mm to 40mm of rain quite widely on Friday and as much as 60mm possible over some hilly areas, with the same amounts for Saturday.
It said: “Further persistent rainfall, heavy at times, will occur through Saturday afternoon and into early Sunday morning.
“Further snow melt is likely across the Southern Highlands, contributing to the flood risk.”
The Scottish Environment Protection Agency has flood warnings in force in Callander, Aberfoyle and Newton Stewart, and on stretches of the rivers Tay, Tummel, Isla and Lyon in Perth and Kinross.
There are also warnings for the Whitesands area of Dumfries, several parts of the Borders, Strathglass in the Highlands and the South Esk river in Angus.
Network Rail said the Ardrossan-Largs line was now expected to remain shut for up to another four weeks after three landslides a fortnight ago.
But trains will resume as far as West Kilbride from Monday after the two more minor landslips are cleared.
However, some 4,000 of debris also fell near Fairlie, with 100m of hillside above the track needing remedial work.
A further landslip in the Borders, affecting the A7 between Langholm and Hawick, was cleared overnight.
People in western parts of Scotland are also being warned to brace themselves for very strong winds and blustery weather from Saturday evening, continuing into Sunday.
The Met Office has issued yellow warnings for wind covering the Highlands and Islands and Argyll and Bute.
Forecasters said gusts could reach more than 70mph in places, with exposed coasts likely to most affected.
CalMac cancelled all sailings on both its routes to Arran along with those to Barra, Bute, Colonsay and South Uist.
Mallaig sailings to Armadale in Skye and the Small Isles were also suspended, together with those on the Tarbert-Portavadie and Gourock-Kilcreggan routes.
Meanwhile, Traffic Scotland has cautioned motorists to drive with care and check for potential restrictions on bridges across Scotland, including the Queensferry, Forth, Kincardine, Clackmannanshire, Erskine, Tay, Kessock, Skye and Dornoch crossings.
Further disruption due to stormy weather is expected during the week, with strong winds and persistent heavy rainfall forecast to hit southern parts of Scotland on Tuesday and Wednesday.