A warning has been issued for Cramond meaning that according to forecasts flooding is imminent.
A further warning has also been issued for Musselburgh with SEPA warning that flooding of low-lying properties on the east side of the river in and around Station Road, Eskside East, Millhill, the Roadway between Shorthope Street and High Street is now possible.
There is also a risk of flooding to low lying properties on the west side of the river including those in around Eskside West and the roadway between New Street and Eskside West.
Access to these arenas may be cut off as a result of expected flooding warns SEPA.
Train services were also disrupted by the weather, including the Edinburgh to Glasgow Central via Shotts, Edinburgh to Glasgow Queen Street via Falkirk High and Glasgow Queen Street to Alloa/Aberdeen/Inverness services.
ScotRail tweeted that “there’s disruption on many routes this morning due to extremely heavy rain”.
Throughout Scotland, SEPA has issued 15 flood warnings and 5 flood alerts across Scotland, mainly in the South of the country.
Scotland’s Transport Minister Graeme Dey said: “The conditions could potentially bring disruption to the trunk road and rail networks, so it’s important people plan their journeys before they set off.
“Motorists should make sure their routes are available, follow travel advice from Police Scotland and drive to the conditions. The Traffic Scotland Twitter page is regularly updated and the mobile website – my.trafficscotland.org – lets people access the latest information.
“If you are planning to travel by rail, please check with your operator ahead of your journey. This is particularly important for cross-border travellers following the earlier disruption to services.”
Other areas put on under alert include Dumfries and Galloway, West Central Scotland, Ayrshire and Arran and the Scottish Borders.
SEPA has asked people to remain vigilant stating: “it is your responsibility to take actions which help protect yourself and your property”. Further advice and information is available through Floodline on 0345 9881188.