"You expect that behavior from a child perhaps, but not from an adult," said zoo visitor Stephanie Christensen.
Zoo leaders say luckily the elephants were unfazed and the woman was not hurt.
She told security she is mentally ill and was not taking her medication.
"The only way to really exclude everybody all the time is to put up solid, physical barriers around these spaces and of course that's not what a zoo is about," said zoo director John Lewis.
But this isn't the first incident where the barrier between zoo animal and zoo guest has been breached.
Back in 2007, Reggie the alligator went missing from his enclosure and zoo keepers had no idea where to find him.
In 2004, Gracie the chimp made a brief great escape.
And about a decade ago, Evelyn, a 200 pound gorilla, used overhanging tree branches to make her break.
"You can protect against the most forseeable, and it would be negligent not to," said the Society for the Prevention of Cruelty to Animals advocate Madeline Bernstein.
Bernstein says this latest incident shows that changes are needed.
"I would be really surprised if this is as good as it can get, because clearly it didn't work," Bernstein said.
Meanwhile, the L.A. Zoo feels there is not a lot it can do. A zoo spokesman also said that incidents such as these are extremely rare.
City leaders say they'll work with the zoo on possibly adding security.
"We're going to look at everything, and if there's anything obviously that should be done. But if someone wants to jump over a fence and go climb through another fence, they may be determined to do that, but it's wrong and I hope it doesn't happen ever again," said L.A. City Councilman Tom LaBonge.