British Transport Police (BTP) say it is among a number of concerning incidents around Scotland over the weekend, which included an incident in Glasgow where two youths were lying on the tracks.
The force has issued a statement reinforcing the dangers of Scotland's railway after the incidents.
According to BTP the Falkirk Grahamston incident happened on Thursday at 7.26pm.
BTP is also asking parents to remind children about the dangers that railways can present.
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Superintendent David Marshall, BTP head of operations in Scotland said: "This type of behaviour is incredibly dangerous.
"Trains travel at high speeds, have a long stopping distance and they cannot swerve out of the way.
"Some of the railway is also electrified, meaning overhead power lines are installed which carry 25,000 volts."He added: "Coming into contact with this equipment or being hit by a train would have life-changing consequences, cause devastating injuries and can be fatal.
"It's extremely concerning that there have been these incidents over the weekend.
"Too many times we have seen the tragic consequences of children ignoring the warnings and taking risks that have resulted in terrible injuries or death."
Between January and September this year, there have been 786 recorded trespass offences on Scotland's railway - an 11% decrease due to lockdown with levels much lower in April and May.
Of this year's offences, 219 (28%) were committed by children.
Superintendent Marshall said: "We are asking parents and carers to speak to their children about the dangers and how important it is to stay safe.
"BTP will be conducting additional patrols across the network in response to these recent incidents, and anyone found to be trespassing will be prosecuted.
"Normally BTP officers would be visiting schools across Scotland to meet children face-to-face and talk to them about how we keep people safe on the railways, and how they can keep themselves safe.
"Due to Covid we are unable to visit schools so I strongly urge parents and carers to check where their children are going and remind them of the extreme dangers posed by the railway."