British Transport Police are treating the incident as “public indecency” and appealing for help to trace the man.
The woman was on a train travelling between Polmont and Edinburgh Waverley when she fell asleep at 7.21am on April 20.
When she woke up a man was sitting next to her naked.
He later put on jogging bottoms and a T-shirt before leaving the train at Edinburgh Waverley.
The man is described as white, of medium/slim build, aged 65-70, 5ft 6 inches tall with short grey hair and a stubbly beard.
He was wearing black joggers, a black T-shirt and black walking boots.
Anyone with information is asked to contact BTP by calling 0800 40 50 40 or by texting 61016 – with reference 2300044058 or Crimestoppers on 0800 555 111 where anonymity can be maintained.