Speaking to the New York Times, Ms Stone said the alleged incidents happened in 2010 and 2011 during production of The Diary of a Madman at Sydney's Belvoir Theatre.
The actress alleges the star would send her "affectionate and flirtatious" text messages that were sometimes sexual in tone, although she "bantered" with Rush as to not upset him.
"He was obviously incredibly invested in this show, which for all intents and purposes was his show, and I would be supporting him in that," Ms Stone told 7.30.
"That was very much the dynamic of the room, that we were working around Geoffrey's performance.
"[I was] very inexperienced, he was this person who is an internationally lauded star, he's pretty much won every award you can win."
Over time, the banter took an edge that made Ms Stone uncomfortable.
"They [the text messages] became increasingly sexual in nature," she said.
"I was very willing to accommodate all this behaviour, I was enthusiastically trying to keep up with this banter."
"I didn't know how to stop the texts," Ms Stone said.
She further alleges Rush danced completely naked in front of her, and once while bathing she saw a "small shaving mirror over the top of the partition between the showers", which she believed he was using to peek on her.
"I said some words to the effect of, "Bugger off, Geoffrey." I was walking a very delicate line where I needed to manage these uncomfortable moments but never, never offend him."
Rush told the Times: "… the allegations of inappropriate behaviour made by Yael Stone are incorrect and in some instances have been taken completely out of context.
"However, clearly Yael has been upset on occasion by the spirited enthusiasm I generally bring to my work.
"I sincerely and deeply regret if I have caused her any distress. This, most certainly, has never been my intention. When we performed in The Diary Of A Madman eight years ago, I believe we engaged in a journey as artistic comrades."