Police forces across the country are taking part in Operation Sceptre, which runs this week.
Since April 2016, there have been 41 recorded knife incidents on the railway in Scotland.
Police activity this week is intelligence led and officers are working to engage with the rail community, including rail staff.
Inspector Richard McCartney from BTP, said: “Thankfully, our statistics tell us that knife crime on the Scottish railways remains low. And where incidents are recorded, the majority are for possession offences rather than a knife being used as a weapon.
“Nevertheless, we recognise that BTP has a pivotal role in tackling knife crime and the devastating consequences that knife crime can lead to.
“That is why we are supporting this national week of action in Scotland.
“There can be no excuse for being in possession of such a lethal item. Our tactics are designed to make the railway a hostile environment for criminals to operate.”
During this week, officers will be highly visible at stations, looking to engage with the travellers and to deter and disrupt knife crime.
Insp McCartney added: “A main focus for us will be talking to people at stations and on trains, particularly young people who are more likely to be carrying knives.
“We are aware there are many reasons why a young person might carry a knife and we are working with community groups and safeguarding teams on these issues.
“We want people travelling on the railway network to feel safe and reassured by the action BTP officers are taking alongside our colleagues in other forces and partner agencies.”