Marcus Mars, 34, disappeared from an address in Talygarn, Pontypool, last Sunday.It's thought he could now be in the Hampshire area.
Police made diligent inquiries locally before spreading the search across a much wider area.
Marcus (pictured) is described as being white, approximately 5ft 8ins tall, with short/shaven brown hair. He is normally clean-shaven although he may now have slight facial stubble.
Marcus was last known to be wearing a red hooded top and pale trousers, and was carrying a blue holdall/rucksack labelled "Aquatec." It is believed he may have got on a train in Cardiff on Monday and travelled to Southampton.
A police spokesman said, "We are concerned for Marcus' welfare because he does not have his medication with him."
He remained missing as the Chronicle went to Press on Wednesday. Anyone with information relating to his whereabouts is asked to call 101. quoting log 418 of May 31.