It is being treated as a missing person search but so far no one has been found.
Police, coastguard and lifeboat teams have been involved in the search operation.
A police helicopter was reportedly seen above Broughty Ferry and Monifieth on Monday as part of the same investigation.
A Police Scotland spokesperson said: “We can confirm that searches are continuing today (Tuesday) following a reports of concern for a man who seen on the Tay Road Bridge on the evening of Sunday.
“Officers have been assisted in these efforts by specialist colleagues, air support and the coastguard.”
A spokesperson for the coastguard confirmed one of its helicopters is being used in the search.
She says the search is being led by Police Scotland and the organisation has nothing further to add.
River Tay search continues after concerns raised for man at road bridge