"Anything & Everything" appears to have been the world's first rock musical, with book and lyrics by Ted Nelson and music by Richard L. Caplan.
 

I have seen no indication that there was any earlier rock musical-- meaning a show with rock'n'roll songs, scenes, characters and a plot.  (As distinct from a rock concert.)

Why would anyone have heard of it?  It ran as scheduled for two nights as scheduled at Swarthmore College on November 21 and 22, 1957.  The well-known rock musicals began with "Bye Bye Birdie" (1960) and went on to "Hair", "Joseph and the Technicolor Dreamcoat," "Tommy" and "Jesus Christ Superstar."

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MP3s for you from "Anything & Everything," the world's first rock musical, 1957--

"It's Not Bad Being Out of College."  Vocalist: Richard L. Caplan.
"Song of Significance."  Vocalists: Bob Caplan, Dave Tucker, Ted Nelson, Richard L. Caplan, Chorus.

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I was a junior.  I explicitly wanted to write the world's first rock musical.  "Oh, rock and roll won't last," I was told by many fellow students.  "It will," I would reply, echoing the sentiment of the song "Rock and Roll is Here to Stay."

Caplan was a freshman whom I recruited.  He proved very talented at providing exactly the music I wanted.

I had been deeply moved the previous year by Brecht and Weill's bitter Dreigroschenoper (the Blitzstein translation to English, "Threepenny Opera," was a big hit off Broadway in '56).  Threepenny Opera was very anti-middle-class.  I asked Caplan to write rock tunes and arrangements that sounded like Threepenny Opera, and so he did.  (The Second Act Finale, entitled "Song of Significance," is explicitly based on the very harsh Threepenny song "Ihr Herrn die uns lehrt wie Mann brav leben," translated by Blitzstein as "O those among you full of highest teaching.")

The first two acts were a satire on Swarthmore (called in the show "Wrathsome"), and the unfortunate third act added a plot about spies on campus.  It was much too long, and the size of cast, crew and orchestra (some seventy people) outnumbered the audience.

The LP was offered under the Truly Zorch label (another early innovation-- the silly record company name).  Some of the songs are still pretty good, though the record itself-- done with very little rehearsal-- has its unfortunate aspects.
 

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We plan to sell the few remaining LPs of "Anything & Everything," one at a time, on Ebay, if and when we have time.  (They will be sent from California by our assistant Litta Rascal.)