Slapping the back of his guitar for extra percussion, Presley invented a new style for himself with his take on this song by blues singer Blackwell. "Don't Be Cruel," backed with "Hound Dog," was a double-sided smash on the pop, R&B and country charts. Its 11-week domination of the Number One spot was the longest in history - until "End of the Road," by Boyz II Men, broke that record in 1992.
~Source RollingStone.com

Don't Be Cruel was released as a single with "Hound Dog." It is the only single in history to have both sides reach #1 in the US.

Billboard's 'Best Sellers in Stores' chart listed the the #1 song on 8/18/56 as 'Hound Dog/Don't Be Cruel.' It was also shown that way when it first topped the 'Most Played in Juke Boxes' chart on 9/1/56. There is absolutely no doubt that the initial sales and 'buzz' about this record was for 'Hound Dog.' It was a smash #1 hit right out of the box. As airplay began to favor 'Don't Be Cruel,' the two titles were flip-flopped at #1, with 'Don't Be Cruel' actually showing more weeks as the #1 lead song.
~Source: SongFacts.com