Disgraced YouTube star Logan Paul says he wants to join the expedition so he can "find the facts" behind their theories.
FEIC founder Robbie Davidson told Forbes: "If you take a globe and you squish it down, the Antarctic would go all the way around the Earth.
"It's kind of like an ice shore, and it's very, very large. It's not like you just go there, and you can just peek over it.
"We don't believe anything can fall off the edge because a big portion of the Flat Earth community believes that we're in a dome, like a snow globe.
"So the sun, moon and stars are all inside. It's very high but all contained inside. So there's no way to actually fall off of the Earth."
However, many have pointed out the ship taking them will use navigational equipment that counts on the Earth being a sphere.
Global position systems use a network of satellites that orbit the Earth to ping off each other to pinpoint a location.
Speaking to The Guardian , Henk Keijer, a longtime cruise ship captain, gave his thoughts on the FEIC's plans.
"I have sailed two million miles, give or take," he said.
"I have not encountered one sea captain who believes the Earth is flat."
Two women wearing Flat Earth T-shirts at a Flat Earther meet-up. Photo / Getty Images Flat Earthers believe Nasa has duped people into believing that the Earth is round and that the theory is a way governments can keep control.
The Flat Earth Society suggests "the space agencies of the world" conspire to fake "space travel" to hide the Earth's "biggest secret".
"This likely began during the Cold War," the Flat Earth Society says.
"The USSR and USA were obsessed with beating each other into space to the point that each faked their accomplishments in an attempt to keep pace."
Some bizarre theories from Flat Earthers include not being able to see a curve in photos or while travelling or that images of Earth in space are computer generated and not real.