Police are investigating a report of public order which occurred on Tarn Fell, Brampton.
The incident occurred between 11.30am and 11.45am on Saturday 7 November.
Information was received from two female walkers reporting that a man had approached them, as they were on the approach to the stone circle on the fell.
A Cumbria Police spokesman said: “The man was verbally abusive towards them, making remarks of a sexual nature.
“The man is described as having dark hair and of an approximate age of 40. He was dressed in black lycra-type clothing and black trainers. He was also wearing headphones which looped around his ears.
“Officers would like to speak to any witnesses to the incident or anyone who had seen a man matching the description provided.”
Anyone with information is asked to contact police on 101 and quote incident number 100 of 7 November. Alternatively you can contact Crimestoppers, anonymously, on 0800 555 111.