 Bayliss (left) and Jayawardene meet the Australian press in Adelaide |
Jayawardene's side arrived down under on Wednesday ahead of a two-Test series and he insists they have the bowlers to test the world's number one outfit.
Off-spinner Muttiah Muralitharan will complement a four-strong seam attack and Jayawardene said: "We have proved we can handle pace and bounce."
Coach Trevor Bayliss added: "Our pace bowling attack is extremely strong."
The Sri Lankans kick off their tour with a warm-up three-day match against Queensland on 2 November, before Tests from 8 November and 16 November.
The tour precedes their home series against England and Jayawardene believes his side can stand up to the task against Australia, who have not lost a home series since 1993 against the West Indies.
Australia will also be without recently retired paceman Glenn McGrath and spin legend Shane Warne.
"I think with Glenn and Shane not being there, they probably lack a bit of experience in their bowling attack, that is an area we can look forward to," said Jayawardene.
"But Australia have still got a very good side. We have to challenge them in bowling, batting, fielding and mentally be very tough under different conditions.
"It's not just one area, but if you are to beat Australia in Australia, you have to play your best game possible."
Conditions in Australia have historically been tough for Sri Lanka, with Muralitharan in particular taunted by home crowds on previous tours.
But Bayliss hoped the majority of people would respect his side, saying: "There's always idiots in every crowd, but most realise it's wrong and don't get involved."
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