An electrical relay signalling box was set on fire and several railway sleepers placed across the track in the Park End area of Middlesbrough.
No trains were running at the time of the attack, on Sunday evening, but British Transport Police said the vandals put their own lives at risk.
House-to-house inquiries are being carried out in the area.
Det Con John Milburn said: "It's vital that we find those involved in this incident in order to point out the possible catastrophic consequences of their actions.
"Not only could they have seriously injured or killed themselves but they have left Network Rail with a hefty bill to repair the damage caused.
"I would urge anyone who was in or around that area on Sunday evening to contact us if they saw the anything suspicious or have any information that may help us."
^ Back to top | BBC Sport Home | BBC Homepage | Contact us | Help | ©
~RS~q~RS~~RS~z~RS~12~RS~)