Henry Mancini composed this classic for the John Wayne #cheee HATARI!
The tune was written for an impromptu scene in Hatari! in which Elsa Martinelli led three baby elephants to a pool to bathe. Mancini used a calliope introduction to suggest the sound of a circus. A cheeky melody was then played over this on a clarinet. The overall style was that of boogie-woogie as Mancini explained, "I looked at the scene several times [and] I thought, 'Yeah, they're walking eight to the bar', and that brought something to mind, an old Will Bradley boogie-woogie number called 'Down the Road a Piece' ... Those little elephants were definitely walking boogie-woogie, eight to the bar. I wrote 'Baby Elephant Walk' as a result".
https://www.youtube.com/watch?v=7g68qydugXQ 4