Clarets’ boss Eddie Howe has offered new contracts to Wes Fletcher, Dominic Knowles, Alex-Ray Harvey and Alex MacDonald.
The four young prospects have all been offered 12-month deals to stay on at Turf Moor.
But second-year professionals Chris Lynch, Nik Kudiersky and Chris Anderson have been released, along with first-year pro Michael King.
“It’s tough to make these decisions,” said Howe.
“But hopefully the four players offered deals will have the chance to progress further with us next season and we wish the others all the best in their future careers elsewhere.”
Frontmen Fletcher, 20, and Knowles, 19, have both been involved with the Clarets’ first-team squad in the closing weeks of the season, as well as featuring for the reserves.
Young striker MacDonald, 21, is currently on loan at Scottish Premier League side Inverness Caledonian Thistle, while midfielder Harvey, 21, is gaining first-team experience at Fleetwood Town.
Defenders Lynch and Kudiersky and midfielder Anderson end their lengthy stays at Turf Moor, having progressed through the club’s youth system.
And winger King, 19, leaves after making one senior appearance as a substitute in Burnley’s Carling Cup tie at Morecambe last August.