The Royals won the Championship title last year but will make an immediate return to the second tier after finishing 19th.
The Berkshire club's plans for the new campaign are underway and they have announced that left-backs Harte, a former Ireland international, and Shorey, who won two caps for England in 2007, will not have their contracts extended past the summer.
Irish striker Hunt will also be leaving the Madejski Stadium, as will Simon Church and Jay Tabb.
Joseph Mills is another out of contract and is set to join Burnley on a two-year deal, having spent the season there on loan.
Youngsters Charlie Losasso, Angus MacDonald, Josh Webb and Brett Williams will also depart, although six out-of-contract players have been offered an extended stay.
Former Arsenal goalkeeper Stuart Taylor is the most high-profile player asked to stay, while Jonathan Henly, Lawson D'Ath, Nick Arnold, Shane Griffin and Matt Partridge are also in talks with the club.