The man was seen "acting suspiciously" by a 45-year-old woman walking her dog near Spink Path, Arbroath, at around 1.20pm yesterday, Police Scotland said.
The scene is known as the "dammy area" and is close to a children's play park.
The man is believed to be aged in his early to mid 20s, about 5ft 7ins tall, heavy build with a "pot belly".
He has brown or fair hair in a style which the witness described as a "mop head". He is also believed to speak with a local Scottish accent.
The weather was sunny and warm at the time and there would have been a large number of people attending or passing through the area, police said.