Local residents have objected to the plan for the erection of a new stadium at a cost of more than €300 million.
The oral hearing gets under way at the Gresham Hotel in central Dublin at 10am and is expected to run for a week.
The redevelopment plan submitted by the soccer and rugby representative bodies would create a 50,000 all-seater stadium.
Currently, Irish international soccer and rugby games have a capacity of 36,000.
While both the FAI and IRFU will contribute to the financing, nearly €200m is to come from the Government.
While the plan was passed by Dublin City Council, this decision has now been appealed to An Bord Pleanála.
Among concerns are the stadium height, the demolition of a house on Shelbourne Road, flooding consequences and loss of part of the Dodder walkway.