The Wallabies go into a repeat of the 1991 and 2003 semi-finals on the back of an uninspiring World Cup campaign to date, with defeat to Ireland ensuring they failed to top their pool and therefore avoid a clash with the All Blacks until the final.
Victory over reigning champions South Africa in the last eight owed a great deal to good fortune after the Boks dominated possession and territory but former skipper Elsom says they are under no great pressure to suddenly recapture the kind of form that secured a first Tri Nations crown in a decade less than two months ago.
Instead, Elsom echoed what most of the world's media has been suggesting since the All Blacks' quarter-final exit to France four years ago - that no side has ever been under as much pressure as the Kiwis to deliver.
"They're the number one-ranked team in the world and they're in a country where they expect them to win the World Cup," said Elsom.
"Regardless of what happens, the public expect that. I can't speak for them, but I know you get a feeling around town that they won't tolerate anything less.
"The situation is that not only are they expected to win this match but then the next one as well.
"There is a hell of a lot of expectation. Just what that does to them, I'm not sure, but you definitely know it's there."
Those sentiments were echoed by fly-half Cooper, who knows all about pressure as he continues to face masses of criticism for his personal displays at his first World Cup.
Cooper has been one of the Wallabies' standout performers since late 2009 but his form has slipped substantially during the tournament.
But while much has been made of Cooper's poor performances, the man himself says the pressure on him is nothing compared to that faced by the All Blacks.
"They're supposed to have won this World Cup for the past three tournaments and this is no different," said New Zealand-born Cooper, who claims he is far more interested in a Wallaby win than a man-of-the-match outing, although he does admit that if he did score in an Australian victory it would simply add insult to injury for the Kiwis.
"A lot of pressure is on them to win this competition on home soil.
"Me scoring would be a tough one for them to swallow. But I'm sure they've got a lot more things to worry about than myself.
"Having a good game is going to play second fiddle to winning the game. I don't care if I have a shocker and we win as a team. I'd much rather walk off the field as a winning team than having the greatest game of my career and we lose.
"These are the moments you play rugby for, for an opportunity to play against the best team in the world, right in their backyard, in the World Cup semi-final. You can't picture it any better than that."