The subterranean tube system is designed to transport electric cars through cities at high speed.
Reporters and guests took some of the first journeys in the tunnel system, which is currently only a mile long, beneath the surface of Los Angeles.
Mr Musk hopes that vehicles in the tunnels will eventually hit speeds of 150mph when the network has been developed further.
During the test ride cars travelled at 40mph. The top speed of the London underground is 60mph.
Cars enter the tunnels through a wall-less lift which slowly takes cars down a wide shaft, roughly 30ft below the surface.
The cars, which need to be autonomous, then speed up when they enter the system.
Guests who tested the tunnels said the vehicle jostled significantly during the journey, which was bumpy enough to give one reporter motion sickness.
Tech entrepreneur Mr Musk described his first journey as ‘epic”’.
He told reporters: ‘For me, it was a eureka moment. I was like: ‘This thing is going to damn well work.’’
He said the journey is bumpy at the moment because ‘we kind of ran out of time’, and there were some problems with the speed of his paving machine.
Of future systems, he said: ‘It’ll be smooth as glass. This is just a prototype. That’s why it’s a little rough around the edges.’
Later, Mr Musk emerged from the tunnel himself inside one of his cars before giving a speech about the technology.
He said: ‘Traffic is soul-destroying. It’s like acid on the soul.’
The entrepreneur explained for the first time in detail how the system, which he simply calls ‘loop’, could work on a larger scale beneath cities across the globe.
Autonomous, electric vehicles could be lowered into the tunnels on the special lifts.
The cars would have to be fitted with specially designed side wheels, fitted to run along the tunnel’s track.
The cost for such wheels would be about £158-£237 per car, Mr Musk said.
A number of autonomous cars would remain inside the tunnel system just for pedestrians and cyclists. Once they are within the main arteries of the system, every car could run at top speed except when entering and exiting.
For the privately-funded test tunnel, Mr Musk acquired a tunnel-boring machine which had been used in a San Francisco Bay Area building project and put it down a shaft in a car park at the SpaceX headquarters.
Mr Musk said he is hoping that an extensive network will be open in Los Angeles before the city hosts the 2028 Olympics.
He said: ‘Wouldn’t it be incredible if you could travel around LA, New York, Washington DC, Chicago, Paris, London – anywhere – at 150mph?
‘That’d be phenomenal.’