The crash happened on the A720 near the Baberton junction on Thursday afternoon.
Pictures appear to show one of the cars skidded into the hard shoulder with significant damage to its bonnet.
It is understood that there have been no serious injuries following the crash.
A Police Scotland spokeswoman said: “We were called at around 3.30pm to a two-vehicle crash.
"The vehicles are on the hard shoulder and it doesn’t appear that there are any serious injuries.”
Traffic Scotland has reported congestion on the A720 westbound at Sheriffhall to Baberton and eastbound from Gogar to Barton.
Congestion has also been reported on the bypass westbound at Sheriffhall between Lothianburn and Babertion as well as eastbound at Calder to Baberton and Gilmerton to Sheriffhall.