Two victims - both 13 - received electrical burns near the tracks in Wednesbury at around 11.45am on Thursday close to the Bescot Stadium station.
Network Rail said that 25,000 volts pass through the overhead wires on the track.
British Transport Police have said that the boy who was critically injured, and is now stable, received severe burns.
After the incident, the seriously injured boy was flown to Birmingham Children's Hospital by air ambulance next to Durham Road.
Leader of Sandwell Council, Steve Eling, said: "The railways are incredibly dangerous. People don't realised just how dangerous it can be on a railway.
"It's about keeping kids safe. If parents knew their kids were going onto a motorway they'd do something about it so we need the same attitude with railways.
"We all hope they make a good recovery as soon as possible."
One neighbour, who asked not to be named, said: “The police told us that they were playing with a stick and touched a live wire.
"A lot of the kids go over and mess around there because there’s a gap in the fence."
Enquiries and an investigation is still on-going and British Transport Police are in discussions as to whether further action will be taken in regards to the land and fencing.
Jacqueline Wilson, acting inspector with the force, said at the time: "There’s a full investigation on-going, all I would like to say is that it is the school holidays and it’s always a time where we have increased trespassers.
"Children are fascinated by the railway but we’ve got to remember it’s real wires it’s real trains and it’s not a playground.
“We can’t fence every inch of the railway off. It gets damaged by people daily wanting to take short cuts. We’re just getting across to them how dangerous it can be."
Another resident said: “Loads of neighbours came outside. The helicopter landed on the grass and we saw one boy put into the ambulance with leg and arm burns and the other had burns to his face and was airlifted.
“We’ve lived here for around 10 years but don’t think anything as serious as this has happened on the train tracks.”
Train operator London Midland said all lines between Bescot Stadium and Tame Bridge Station were blocked after the incident.
Network rail say journeys between Birmingham New Street and Walsall were disrupted while the service recovered.
There were expected delays of up to 25 minutes and cancelled services. A normal service resumed around 3.30pm.