The 26-year-old woman was at Cambuslang train station on Tuesday, June 10 with the youngsters when the man flashed at them.
He is believed to have then boarded a train to Rutherglen where he was again seen acting in a suspicious manner.
British Transport Police is now appealing for witnesses to the incident, which happened around 11am.
The man is described as being about 5ft 6in in height, with short dark hair, thin build, sallow skin and wearing a striped top and dark trousers.
Detective Constable Ryan Tierney, the BTP officer in charge of the enquiry, said: "There is no excuse for such unsavoury behaviour and I am appealing for anyone who was at either station or on the train and can provide information which could identify the man responsible to come forward."
British Transport Police can be contacted on 080 40 50 40 or by texting 61016.
Information can also be given anonymously to Crimestoppers on 0800 555 111.