One resident in Balcarres Street said her ground-floor-flat had been ruined following the flash flood at 1440 BST.
Emergency council teams have been deployed in a bid to help firefighters deal with the "huge volumes of water".
A resident in Balcarres Street added that the fish in her pond in her front garden had been washed away in the flood water.
A 31-year-old witness said: "I have never seen anything like it. There was such a huge volume of water in Balcarres Street that buses were trying to plough through it and the wake was causing the cars at the side of the road to crash into each other.
"There is also a car showroom in the street, which has been flooded."
One person Tweeted that a car had been picked up by the flood water and "washed down" Comison Road.
Others said they saw wheeliebins floating down roads in the south of the city.
Fire crews were also sent to the Edinburgh Prison Officers Club on Longstone Road in Saughton.
The bar area was flooded, which was pumped out by two lines of hose.
An Edinburgh City Council spokeswoman said: "Following very heavy rain this afternoon certain areas of the city have experienced flash flooding.
"The worst affected areas are in the south and west of the city.
"We are receiving a significant volume of calls from residents and businesses and have deployed emergency staff to provide assistance."
Lothian and Borders Fire and Rescue Service said it was "busy dealing with flooding in large areas of Edinburgh after torrential rain".
George McKendrick, operations manager for Lothian Buses, said: "From 1500 BST on Friday, a number of services in the south and west of Edinburgh were diverted due to the rain and subsequent flooding.
"The control room team has been working with drivers and staff on the ground to create the most suitable diversionary routes for our passengers.
"We have deployed all spare Lothian Buses vehicles to cover services that have been disrupted and to alleviate late running buses.
"Services 5 and 16 were diverted at Greenbank because the Braid Burn burst its banks, while Balcarres Street in Morningside was flooded, resulting in the service 23 terminating on Morningside Drive.
"One of our buses was stuck in Balcarres Street and has been flooded but the water has caused no damage to the bus."
He added that the nearby Craighouse Campus of Napier University was closed due to a manhole cover being forced open by the flooding.
Craiglockhart Campus has also been closed. Both of these incidents caused diversions for Lothian Buses and service 23.
In Slateford Road there was flooding and service 4, 34 and 44 were diverted via Chesser and Longstone Road.