Hospital bosses expect the third wave to arrive in the middle of January, as a result of restrictions being eased over the Christmas period.
Chief executive of York Teaching Hospital NHS Foundation Trust, Simon Morritt, says tackling a second wave has been “very challenging” for staff.
And he confirmed that he has been asked to start planning for a third wave of infections due to peak in the first weeks of 2021.
The Trust also runs services at Bridlington and Malton hospitals.
Mr Morritt, speaking at a Trust council of governors meeting on Wednesday, said: “The expectation is there will be a third wave, perhaps related to some of the easing of restrictions around Christmas.
“We are currently in the second wave. We are on the downward trajectory, although it’s a slow decline.
“It’s probably true to say things have been more challenging on the east coast than in York this time around.”
At the peak of the second wave last month, there were around 130 coronavirus patients in York and Scarborough hospitals.
The Trust created space for up to 197 Covid patients during the second wave.
Mr Morritt said the number of inpatients has now fallen to 85.
“As with the first wave it’s been a very challenging time for all staff, but my sense is we have coped well,” he added.
“We have delivered services in very trying and challenging times.
“Communication has been better and we have learned lessons from the first wave.”
But he said the Trust is still waiting for confirmation of when residents will start to get the Pfizer vaccine.
He said: “We are still awaiting confirmation from the vaccine centre about when we can expect to receive a supply."