The men, aged 22, 28 and 53, were arrested Thursday and arraigned in court later in the day.
Police say the men lifted a manhole cover and went into a secure area of the metro system.
They filmed themselves wandering through maintenance tunnels, went onto the tracks used by the metro trains, and once on the trains walked from car to car, and into the control booths used by metro drivers.
Two of the men were also charged with possessing burglary tools.
After the video was posted online STM officials welded the manhole covers shut so nobody else could use them to access the tunnels.
The three men are due back in court on May 5.