Train windows have been smashed and museums raided while a £100,000 emergency appeal has had to be launched to repair storm damage.
The incidents have affected largely volunteer-run routes in the Borders, Ayrshire, Brechin and Bo’ness.
They have come as a further blow after the lines lost key income by being forced to close because of Covid-19.
Worst hit by vandals was the Waverley Route Heritage Association at Whitrope, south of Hawick, which has been forced to stay closed until next year.
Chairman Chris Donnelly said: “Unfortunately, since May we have suffered a considerable amount of trespass and vandalism to rolling stock.
“We have repeatedly been targeted by vandals, who have smashed windows which are not easy to replace on vintage trains, broken into our museum and damaged stock on site.
"It’s really dispiriting to see hard work ruined.
"However, we are determined to continue and have been overwhelmed by the support which we have received from the local community and wider railway family.”The Doon Valley Railway in East Ayrshire, was also attacked.
A spokesperson said: “During lockdown, the railway has sadly been subjected to minor vandalism, with graffiti on one of our wagons and damage to our lineside fencing by trespassers.
“We would like to remind the public that walking on railway lines and yard areas is trespass and is illegal.”
The Caledonian Railway in Brechin has said it has also suffered “thoughtless vandalism that has required the involvement of the police”.
Meanwhile, the Bo’ness and Kinneil Railway has been prevented from reopening by significant damage to the line from landslips two weeks ago.
Amanda Kilburn, business development director of the Scottish Railway Preservation Society (SRPS), which runs the railway, said: “These are hard times for everyone, but a double whammy for us this time.”
During a storm which also flooded the nearby Edinburgh-Glasgow main line from a canal burst, multiple landslips happened over a mile-long stretch.
Ms Kilburn said: “The significant damage to our line could not have come at worse time.
“We had planned a limited reopening of the railway in mid-September after a lengthy closure due to the coronavirus pandemic that has left our income at a record low.
“Until the embankment is repaired, we cannot operate any trains meaning that we cannot generate any substantial income.”
However, a huge response to its £100,000 appeal for repair costs has already seen the target exceeded by £10,000.
SRPS chairman Steve Humphreys said: “It is heart-warming to receive such generosity from people of all ages who want the railway to re-open just as much as we do.
“We have built up a lot of loyal visitors and want to ensure we can welcome everyone back as soon as possible.
“We really want to be able to celebrate the 60th anniversary of our foundation next year with trains running once again.”
The Heritage Railway Association warned people to keep off heritage lines because maintenance trains were running during their closure to passengers.
Scottish committee chairman Peter Ovenstone said: “A problem has been that many people may have assumed that as heritage railways are still closed to the public, no trains will be running.
"The reality in most cases is necessary maintenance trains have been - and will be - operated from time to time.
"The public are urged not to trespass at any time on any heritage railway in Scotland.”
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