The South Australian opposition says videos posted on social media over recent days have shown "massive lines" of cars at various drive-through testing sites.
That has followed three consecutive days of record case numbers including 80 confirmed infections on Sunday.
Opposition Health spokesman Chris Picton says the state government assured the public that authorities were prepared for the opening of borders last month and testing capacity was adequate.
"However, in the past week we've seen South Australians waiting hours to do the right thing and get tested," he said.
"The demand on testing was always going to increase after the borders opened and COVID cases in our community increased."
Mr Picton said the government must urgently provide the resources required to deal with the increase in demand.
On Sunday, 16,879 tests were conducted while on Saturday 19,232 were performed.
It's understood SA Pathology has a current capacity to process about 20,000 swabs each day.
There are some private laboratories also providing testing facilities.
Chief Public Health Officer Nicola Spurrier said it was a case of "all hands on deck for us".
However, she said SA Health was battling a shortage of labour along with other sectors of the state's economy.
"I think there's a shortage of people across the board because our international borders have been shut," she told ABC radio on Monday.
"We have certainly been recruiting and training.
"As a community, we just have to be mindful that there's only a certain number of people in South Australia that can do these jobs."
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