In Victoria, some close contacts who were initially advised to get a PCR test have received text messages from the Department of Health suggesting they get a rapid antigen test instead if they don't have any symptoms.
In New South Wales (NSW), Health Minister Brad Hazzard says wait times for Covid-19 test results have ballooned to 48 to 72 hours, with many people waiting even longer than that to get a result.
The NSW government yesterday urged people to only get tested if they have symptoms, are identified as close contacts, or as part of their travel requirements.
The ACT government is trying to limit the number of people arriving at testing clinics to obtain a "travel test" result, which is needed to enter Queensland, Tasmania or the Northern Territory.
All three open testing sites in Canberra had to close by 9.30am today because they had reached capacity.
Leading epidemiologist Mary-Louise McLaws says there should have been a better plan to deal with the added pressure on testing over Christmas.
"There should have been some planning to understand that Australians would want to go out and get tested before they went to see their families," she said.
"But they have not done that in New South Wales or anywhere in Australia. They should have been giving out free rapid antigen testing before the holidays."