Between 9pm on Saturday 9 March and 6am on Sunday 10 March, waiting shelters, vending machines and equipment were smashed up at Selling, Teynham and Whitstable railway stations.
The damage is believed to be in the region of nearly £6,000.
Officers believe the men in the images may have information that could help their investigation.
Anyone with information is asked to contact BTP by texting 61016, or by calling 0800 40 50 40 quoting reference number 122 of 10 March.
Alternatively, call Crimestoppers anonymously on 0800 555 111.
