A woman who had been travelling on a train between Edinburgh Waverley and Glasgow Queen Street reported the incident after she saw a man carrying out a solo sex act while watching a video on his phone.
This happened around 6.50 pm on July 19, the man was sitting at a window seat in the train, and was spotted performing the act between Polmont and Falkirk High.
He has been described as white, of medium build, and between 20 and 30 years of age.
He had dark shaved hair in a buzzcut, stubble, and was wearing a tight white top and and light coloured trousers.
Officers are appealing for anyone who may have witnessed the incident to contact BTP by texting 61016 or calling 0800 40 50 40 quoting reference 560 of 19/07/22.
Alternatively you can call Crimestoppers anonymously on 0800 555 111.