I first heard girls scream at the Beatles on the Sullivan Show, but they screamed for other bands as well. When did it become a “thing”? Were girls so excited that they spontaneously started screaming?
Bonus question. What was the last band to be screamed at and when?
The whole idea of young girls screaming at concerts may be entirely the result of a press agent named George Evans and a psychological phenomenon called The Asch Paradigm. In 1942 Evans paid and rehearsed a dozen girls to swoon and scream at a Sinatra concert. By the end of the concert 20 or more non-shill girls were observed to also scream and faint. Within weeks, that’s just what young girls did at Sinatra (and Elvis, and Beatles, and Backstreet Boys, etc.) concerts.
Apropos of your username, see this Merrie Melodies cartoon from 1944, which features “Bobby-Soxer” chickens screaming for a Frank Sinatra rooster (starting about 2:20). He meets his match when a Bing Crosby rooster arrives. (It also features other singers like Al Jolson, Jimmy Durante, and Cab Calloway, as well as a notable use of “Powerhouse” as factory music.)
As far as I know, it hasn’t stopped. For instance, look at some stories on Wand Erection.
Early 60’s rock. Why were the girls screaming?
Sex.
I submit that they didn’t know how to behave at all. This was all new to them, and damned exciting compared to their parents’ world. It was suddenly acceptable to just let one’s self go crazy in public. Unheard of till this generation.
Nope, in fact girls screamed over Rudy Vallee, although Vallee himself said that it was due more to hype than any particular sex appeal he possessed.
According to Leggy Mountbatten, it was the trousers. They were very…tight.
The GQ question has been answered — interesting! — so I can be goofy.
I just assumed they didn’t know the words.
As a caring parental witness I was going to suggest One Direction but Mr Garrison beat me to it.
Lots and lots of screaming for the Monkees when I saw them on the '86 tour.
(Not nearly as much screaming at the 2012 shows 
)
Lisztomania was similar, in the mid 1800s.
Lots of screaming when I saw Ryan Adams a few years ago. Loud enough to drown out the music, very annoying.
They screamed for Sinatra too.
Ha, they probably do the same thing when no guys are around at all. My sister is a fan of this video from some sorority function (don’t ask me what is exactly going on here, but the excitement level goes to 11!): University of Idaho Sorority Recruitment 2012 (Bid Day) - YouTube
“Kindly refrain from throwing soiled breeches”
I don’t know if it’s common in other Asian pop, but when Kpop stars do music shows, there’s amazingly coordinated shouts and screams by the entire audience. Almost surely prompted as it happens less often and at lower intensity at live shows.
Here’s Pristin V performing on a music show https://www.youtube.com/watch?v=W67mLLq7Jes. The chant at the beginning are the members names, then as each singer steps forward for their part, there’s accompanying screams. The audience also sings along with certain parts.
Rudy Vallee was VERY good looking, and knew it. Used to brag about his voice that he had a “cock in his throat.”