The incident happened at about 4.45pm on Saturday in Jamaica Street, Glasgow, near the four corners area.
The boys, aged 12 and 13, were approached by a man who threatened them and stole a mobile phone and a small sum of cash
Neither boy was injured in the incident but police said it had been “very frightening and upsetting for them both”
The suspect is described as white, aged 20 to 29, 5 ft 7in and skinny. He was wearing a Nike top which had a white hood, a red V on the front and then faded to grey at the bottom, grey Adidas tracksuit bottoms with white stripes down the leg and red trainers. He was carrying a JD Sports draw string plastic carrier bag.
Officers investigating the case believe members of the public may have seen the boys around the time of the incident or witnessed it without realising what was happening.
Detective Constable Neil Guy said: “The boys were in town doing a bit of Christmas shopping when they were confronted by the man who took the 12 year olds’ mobile phone from him and cash (two figure lower amount) from the 13-year-old boy.
“There were a lot of people in the area at the time and I would appeal to them to contact police if they can assist with our enquiry.
“One of the boys was wearing a distinctive bright blue ‘bubble’ type jacket which I am sure someone would have noticed. Also, as the suspect bent down to threaten the boys, it may have looked like he was with them - maybe giving them a row. It’s possible someone saw this but not thought much of it at the time.
“Thankfully, neither boy was injured but it was very frightening and upsetting for them both.
“Anyone with information can contact officers at Pollok Police Office via 101 or Crimestoppers on 0800 555 111 where details can be given in confidence.”