Two cars had their windscreens smashed as they passed under the Lanark Road flyover near the turnoff for Baberton.
The Audi A4 and Vauxhall Insignia were targeted on the southbound carriageway of the A720 at around 11.40pm on Tuesday.
Meanwhile, a third vehicle sustained damage to its bodywork when a rock was thrown onto its bonnet.
No one was injured but officers are carrying out various inquiries in an effort to trace those responsible.
They are particularly keen to trace two males seen acting suspiciously under the flyover shortly beforehand.
Anyone who knows who they are or who can help with this inquiry is asked to come forward.
Sergeant Neil Thomson who is based at Wester Hailes police station, said: “These crimes demonstrate a complete disregard for the safety of others.
“Such recklessness is extremely dangerous and could have resulted in multiple serious injuries or worse.
“Our inquiries into this matter are very much ongoing and I am keen to trace two males who were seen in the area of the flyover on Tuesday night.
“I would ask anyone who remembers seeing these individuals or who has information that can assist with our investigation to contact police on 101.
“Alternatively, information can be passed anonymously through the independent charity Crimestoppers on 0800 555 111.”