The vandals have been placing thumb tacks along the A81 route at Bearsden.
Last year, the Herald reported the safety of cyclists was being put at risk through tacks being placed on the lane.
Cyclist Ally Corbett said: “Last Thursday while cycling home on the Bears Way the tyre on my bike was punctured as a result of a thumb tack. When I stopped I found 20 more tacks and fellow cyclists who also stopped, collected dozens more.
“I reported the incident to the police and was told I was the third person to come including a mother with kids in a bike trailer”.
A police spokesperson said: “We are investigating, including looking at CCTV opportunities. Enquiries are continuing at this time”.
East Dunbartonshire Council boss Thomas Glen said: “We have received concerning reports from Police Scotland of tacks being deliberately left on Bears Way, with a number of cyclists suffering burst tyres as a result – including children.
“Such antisocial behaviour is extremely dangerous and the potential to cause a very serious accident.
“The council has been out to sweep the cycle path and we would urge anyone with information to contact police Scotland immediately.”