The team at North Bay Heritage Railway is warning that CCTV or anyone intruding or damaging the railway will be passed on to police.
They are urging parents to warn children not to go onto their site when they are shut.
They have posted on their Facebook page: "We are pleased to say the culprits have been identified by Scarborough Police, we are hoping this will bring to an end the problem we have had over the last few weeks.
"We welcome everyone during our opening times but we have now taken the tough decision to have zero-tolerance of trespass at North Bay Heritage Railway and Lakeside Attractions.
"This covers any area within our perimeter fencing including Peasholm Station, Scalby Mills Station, all the track bed between both stations, area around Boatman’s Tavern, Sky Trail and Water Chute.
"We ask the general public to please only cross the track at Beach Station using the public foot crossing over the track.
"We will continue to monitor our CCTV and will pass any images onto the police if we think there has been trespassing or criminal damage caused to North Bay Heritage Railway property.
"We ask parents to warn their children not to enter our site when we are closed.
"Hopefully we can now move forward and enjoy the last few weeks of the summer with our amazing customers. Please keep coming to North Bay Heritage Railway - every penny will help keep the trains running!"
As reported by The Scarborough News, the railway was hit by vandals on Sunday night when the water chute boat was unshackled, sending it rolling into the lake below.
Because the team removes the boat's plugs at night in case they are taken, the boat sank into the water.
On the previous Sunday yobs kicked out safety screens from one of the carriages parked at the park.
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