The rock group's The Endless River album has put the bandmates in contention for the Grand Design, Best Album and Best Band/Artist of the Year prizes, while Kate Bush is up for two awards, Best Live Event and Artist of the Year, following her return to the stage in 2014, reported Independent.
Devin Townshend, Muse, Marillion, King Crimson, Yes, The Enid and Steve Hackett are also up for top awards.
The 2015 Progressive Music Awards will be held in London in September.