The incident happened in woodland at Newby Hall, the estate near Ripon owned by the Compton family, on Thursday June 30 at 3.40pm.
North Yorkshire Police said: "Around 3.40pm on Thursday 30 June 2022, a naked man approached a group of three women on the woodland walk.
"We are requesting the public’s assistance to help identify the man and in particular, we’re appealing to anyone who’d been at Newby Hall Gardens on the day and may have information which could assist our investigation.
"The man is described as being white, aged 40-50 years old, 6ft to 6ft 2' tall, of a medium build with a slight beer belly and dark brown hair in the style of a short back and sides that had grown out.
"Anyone with information that could assist the investigation should email [email protected] You can also call North Yorkshire Police on 101, select option 2, and ask for PC 1505 Jackson.
"If you wish to remain anonymous, you can pass information to Crimestoppers on 0800 555 111.
"Please quote the North Yorkshire Police reference number 12220113065."