Some reported being groped, while others said indecent comments had left them feeling vulnerable.
The actors' union Equity said it was receiving reports of "more and more" incidents each year.
Police Scotland said it had not received any reports of harassment. It told BBC Scotland that it had an increased police presence.
Most of the abuse is believed to take place on the Royal Mile.
Pressure to "laugh off" harassment
Lizzie - who asked not to use her full name - said she felt she had to go out of her way to behave differently to avoid harassment as she promoted her show.
She told the Victoria Derbyshire programme that while handing out flyers, one man "pretended to brush something off my thigh and then moved his hand, quite forcefully, up my skirt".
On another occasion she was "cornered" by three older men who said they would "only buy a ticket or take a flyer in exchange for my phone number".
She added that men made comments about her appearance and "invaded" her personal space "so their grope could go unnoticed", she added.
Lizzie said that the harsh reality is women put up with it because handing out flyers is the most effective way to sell tickets for lesser-known productions.
One woman said she had felt under pressure to "laugh off" any harassment she endured, such as having her bottom pinched, because she was "trying to get customers".
The actors' union, Equity, said many female performers had become accustomed to abuse.
Its president, Maureen Beattie, said a "slight level of hysteria" at the Fringe "seems to release this kind of underbelly of bad behaviour".
"It is completely and utterly unacceptable. We are a workforce, and you must respect us," she added.
It's estimated that more than 30,000 male and female artists perform at the Fringe each year, across 3,500 shows.
Police Scotland said it had set up two mobile police stations for the duration of August and had increased high-visibility patrols.
It added that it had not received any complaints regarding sexual harassment.
Edinburgh Festival's Fringe Society, which supports the running of the month-long event, said: "Everyone who is part of the Fringe - be they a performer, member of the crew, producer, audience member, critic and so on - has the right to feel safe and supported."
It added that it "takes matters of this nature very seriously" and urged those who experienced inappropriate behaviour to contact police.