Martin Jol's side will be chasing a top 10 finish in the Premier League against the relegated Royals, who begin their preparations for life in the Championship under Nigel Adkins
The seats for the clash at Craven Cottage will be located amongst the home support.
To be in with a chance of winning the tickets, simply send your answer to the following question along with your name, address and telephone number to firstname.lastname@example.org.
Which Reading striker enjoyed a loan spell at Fulham last season?
A) Adam Le Fondre
B) Pavel Pogrebnyak
C) Jason Roberts
The competition will close at 12:00 GMT on Wednesday, May 1, and winners will be announced by Friday, May 3.
Don't worry if you're not successful - you can always win a pair of tickets by visiting your nearest Barclays ATM and requesting a receipt or by going online to www.barclaysticketoffice.com – you don't even have to be a Barclays customer.
Match tickets are up for grabs EVERY 90 minutes, every day, throughout the 2012-13 season.