The SpaceX CEO delivered a speech last month called "Making Humans an Interplanetary Species" at the International Astronautical Congress in Guadalajara, Mexico.
The SpaceX Red Dragon could be sent on an unmanned test mission to Mars as early as 2018.
If everything goes according to plan, the first mission could launch by the end of 2022, although Musk has said the timeline could change.
Musk envisions 100 to 200 people per spacecraft, with the trip taking between 80 and 150 days, depending on the time of the year. Mars is closest to Earth every 26 months, making that an ideal time to make the journey.
Once on Mars, a propellant production plant would be built and that fuel would be used to return the spacecraft to Earth, where they could again be reused to bring back visitors — drastically lowering the cost of a ticket, which he currently estimates at $500,000 per passenger.
Alyssa Newcomb is an NBC News contributor who writes about business and technology.