The competition is intended to appeal to both university students and independent engineering teams, according to SpaceX documents provided to The New York Times.

SpaceX also plans to construct a one-mile test track adjacent to its headquarters in Hawthorne, Calif., which will be used as a testing and competition area for contestants, with a planned start date of June 2016.

The idea appears to be Mr. Musk’s next step in a plan, first proposed in 2013, for a new kind of transportation method that is faster than high-speed rail but slower than supersonic aircraft, that could handle interurban transport for cities about 900 miles or less apart.

Much in the original proposal was not detailed, but Mr. Musk appears to envision cars inside a tube that transfer high pressure air from their front to their rear, and are suspended like pucks on an air hockey table.

The SpaceX Hyperloop Pod Competition, as the contest is called, will probably still draw competitors on the same order as skeptics.

Details like winning rights of way, constructing the tube, creating compressors capable of fueling it, maintaining a constant state of pressure, developing amplifiers or other transit stations to support and service the tube, figuring out and pricing the market, and whether there will be a dining car have yet to be worked out.

SpaceX has said it is not interested in developing a commercial Hyperloop itself, but is interested in helping to produce a prototype. Mr. Musk may simply be trying to kickstart some original thinking to foster development of an industry, as well as attracting engineers to his company. He previously open sourced all of Tesla’s patents with that aim.

In addition, new ideas about ways to transport people through punishing atmospheric conditions could be helpful for SpaceX’s plans to move from launching satellites into manned flight. Mr. Musk is keen to eventually go to Mars. Knowledge gained in the Hyperloop competition, SpaceX said, will be open sourced.

The Hyperloop also has its own Twitter handle, @hyperloop, which may have future news. Full details about competition admissions, which are due by Sept. 15, were not initially available.