Officers say a man used threatening behaviour during an argument with the women at about midnight on Sunday, July 20, on a Waterloo to Reading service.
PC Stephanie Barras from British Transport Police, said: “During the row, he became increasingly aggressive, brandishing a Stanley knife and threatening the women.
“Fortunately he did not make good on his threats, but the women and several other passengers were extremely frightened by his behaviour.”
The man fled onto the tracks at Reading station, before climbing onto platform four, jumping a fence and fleeing in the direction of the Apex Plaza.
PC Barras added: “This man’s behaviour was unacceptable and we need to find him as soon as possible.
“Not only did he scare passengers on the train, he also endangered his own safety by making off across the tracks.
“I believe the man in the images we are issuing today will be able to help with our inquiries into this incident.
“If anyone recognises him I would urge them to get in contact with us.”
Anyone with information is asked to contact British Transport Police on 0800 405040, or text 61016, quoting reference GSUB/B6 of 01/08/2014.
Information can also be passed anonymously to Crimestoppers on 0800 555111.