British Transport Police (BTP) said such alerts had gone up by nearly one-fifth over a six-week period between July and August last year compared to 2013.
The total increased from 148 to 164 in 2014 and 175 in 2015.
However, in the Kilwinning area of North Ayrshire, it went up by three-quarters, from 13 to 23, from seven to 11 around Paisley, and 39 to 50 in Glasgow.
BTP said youngsters were twice as likely to trespass on the railway at this time of year than in the winter.
Incidents have continued this summer, including a group of four children aged about ten trespassing on the West Coast main line near Law in South Lanarkshire on 15 June.
A week later, three girls aged about ten were reported on a line at Carfin in North Lanarkshire.
Other incidents among at least eight last month include four children spotted on the Edinburgh-Fife line at South Gyle in Edinburgh on 30 June.
BTP said playing on or taking a shortcut over railway lines can kill, and is stepping up patrols across the country.
Some 24 people a year are killed on Scotland’s railways, including suicides.
About two-thirds were hit by a train, 17 per cent were electrocuted and others fell from bridges or trains.
Nearly half of trespassers admitted taking a short cut was their main motivation for being on the railway, with nearly one in five saying they were thrill-seeking.
One incident at Wester Hailes Station in Edinburgh in April last year involved two boys aged nine or ten narrowly avoiding being hit by a train.
The next months boys as young as five were caught on CCTV on the tracks.
BTP is urging parents to warn children of the dangers of playing on the tracks.
Chief Inspector Dave Marshall said: “The last thing our officers want to do is knock on someone’s door to tell a parent their child has been killed or seriously injured as a result of trespassing.
“We’re doing all we can to keep young people safe by patrolling areas where we know they’re likely to trespass and prevent them from doing so.
“However, we cover thousands of miles of track and we cannot tackle this issue alone.
“That is why we are urging parents and young people to heed this warning and take a reality check when it comes to trespass. It’s not a game: they are real tracks, with real trains and real-life consequences.”
The figures also showed Edinburgh’s rate remained steady at 27 incidents last year.
There were fewer cases in 2015 than the previous year in and around Aberdeen, Dalmuir in West Dunbartonshire, Dundee, Falkirk, Stirling, and Kirkcaldy. Reports in and around Inverness were up from four to six and there were slight increases recorded in Motherwell and Perth.