In the senior draw Cork Constitution have been favoured with a home draw against Belfast Harlequins and Garryowen will be away to Clontarf.
In the Junior draw, Youghal will be at home to Monivea and Kanturk will have to make the long journey to Magherafelt to play Rainey Old Boys.
All these games are scheduled for the week ending 11th February.
The full draw is
AIB Senior Cup
Terenure College v St. Mary s College, Galwegians v Buccaneers, Clontarf v Garryowen, Cork Constitution v Belfast Harlequins
AIB Junior Cup Draw
Rainey Old Boys v Kanturk, Youghal v Monivea, Westport v Seapoint, City of Armagh v Naas.
The Draw for the semi-finals will be made on Sunday 12th February after the completion of the quarter-finals.