Rampant sexism at it's very VERY best! Hah! 
Great song and we had this at home on a 78 by Bill Hailey and The Comets (of course) but this original is still really worth a listen and no mistake. Superior in every way INMH. Sounds like a New Orleans classic but it ain't, it's Kansas City's finest Big Joe Turner . . . must find out the musicians* but under Ahmet Ertegun's direction you KNOW this was going to rock your socks off!

again from the brilliant Jeff Harris' blog BEHIND THE GROOVES

On this day in music history: April 12, 1954 - “Shake Rattle And Roll” by Big Joe Turner is released. Written by Jesse Stone under the name Charles E. Calhoun, it is the biggest hit and signature song for the Kansas City, MO rhythm & blues legend. Stone (“Don’t Let Go”, “Money Honey”) writes the song after Atlantic Records chief Ahmet Ertegun suggests that he come up with an uptempo blues number for the singer. Turner record the song on February 15, 1954 at Atlantic Studios in New York City. The single is an immediate hit upon its release, spending three weeks at #1 on the R&B chart and peaking at #22 on the pop Best Sellers chart. “Shake” is covered by numerous artists over the years most notably by Bill Haley & His Comets (#7 Pop) and Elvis Presley. Big Joe Turner’s original recording of “Shake Rattle And Roll” is inducted into the Grammy Hall Of Fame in 1998.

* well as usual the entry from Wikipedia is helpful and of interest here and I can't improve upon it after researching:

Turner's version^[5] was recorded in New York on February 15, 1954. The shouting chorus on his version consisted of Jesse Stone, and record label executives Jerry Wexler and Ahmet Ertegün. The saxophone solo was by Sam "The Man" Taylor. Other players included McHouston "Mickey" Baker ("Love is Strange") on guitar and drummer Connie Kay (later from the Modern Jazz Quartet). Turner's recording was released in April 1954, reached #1 on the US Billboard R&B chart on June 12, did not move for three weeks, and peaked at #22, nearly at the same time, on the Billboard pop chart^[6] (subsequently billed as the Billboard Hot 100).The song, in its original incarnation, is highly sexual. Perhaps its most salacious lyric, which was absent from the later Bill Haley rendition, is "I've been holdin' it in, way down underneath / You make me roll my eyes, baby, make me grit my teeth". [It may actually be "Over the hill, way down underneath.] On the recording, Turner slurred the lyric "holdin' it in", since this line may have been considered too risqué for publication. The chorus used "shake, rattle and roll" to refer to boisterous intercourse, in the same way that the words "rock and roll" were first used by numerous rhythm and blues singers, starting with Trixie Smith's "My Man Rocks Me (With One Steady Roll)" in 1922, and continuing on prominently through the 1940s and 1950s. Stone stated that the line about "a one-eyed cat peepin' in a seafood store" was suggested to him by Atlantic session drummer Sam "Baby" Lovett, which is also a sly sexual reference, the "one-eyed cat" being the male organ and the more traditional "seafood" reference being the female organ.