The 38-year-old was walking in the Slateford Green area at around 6pm on Tuesday when she passed the youths, who began to shout at her.
The gang assaulted the woman, knocking her to the ground before robbing her of cash and making off towards the Asda store at Chesser.
One of the suspects is described as male, white, 18 to 19 years old, 5ft 6in with short, bushy, dirty blonde hair. He was wearing a light blue V-necked jumper.
Another suspect is described as female, white, 17 years old, 5ft 4in with a chubby build and dark brown, shoulder-length bobbed hair. She was wearing a lot of make-up.
A police spokesman said: “This was a frightening experience for the woman.”