A fully-stretched NHS trust is starting to transfer patients with Covid-19 to one of the government's emergency Nightingale Hospitals.
University Hospitals Dorset (UHD) NHS Trust said its hospitals in Bournemouth and Poole were "absolutely full" and "on a knife-edge".
The number of patients has risen from "more than 350" to "about 380" in the past week, it said.
Up to 10 patients are due to be moved to the Nightingale Hospital in Exeter.
The move will allow the Dorset hospitals to continue accepting emergency admissions.
UHD medical director Tristan Richardson said: "If we can make that happen two or three times in the next fortnight, I think that will just about see us through but it's still very much on a knife-edge.
"We are absolutely full of Covid patients on both sites."
Senior nursing sister Ann Brown said: "We knew it was going to be much worse than previous winters, however I still wasn't expecting it to be quite this bad."
BBC South health correspondent Alastair Fee, who interviewed staff at the hospital on Wednesday evening, said he saw the pressure building as ambulances delivered more patients with Covid-19.
The NHS trust remains on a level four Operational Pressures (OPEL) alert, denoting potential for patient care to be compromised.
Dr Richardson said: "Speaking to families on the phone when you've said, 'That family gathering you had at Christmas has ended up with your grandparent catching Covid and they are sadly going to die in the next 24 hours', and that penny drops, is sad, so sad."
Nightingale Hospital Exeter is a specialist facility for up to 116 patients with Covid-19 from the south west of England.
It received its first patients in November from the Royal Devon and Exeter NHS Foundation Trust.
In a statement, UHD said: "This joined up regional support will help us to carry on accepting new emergency admissions and providing the best possible care for our remaining patients."
Eyewitness: Alastair Fee, BBC South health correspondent, at Royal Bournemouth Hospital
Coping, yes. But this is also a hospital on the edge.
As the night grew later, I watched as the pressure increased in A&E as ambulances brought in yet more patients with Covid.
In an attempt to ease that pressure, today patients with Covid will be driven to the Nightingale Hospital in Exeter.
Yet again, doctors and nurses stress we can all make a difference - by staying home.