Antrim Area Hospital has warned it is "operating beyond capacity" with 27 sick patients awaiting admission.
Patients have been asked by the Northern Health Trust not to attend the hospital's emergency department unless they require urgent medical care.
The trust said they were clearly "in the midst of the second Covid surge" with many very ill in-patients.
The Northern Ireland Ambulance Service (NIAS) and Southern Health Trust also said they were "extremely busy".
On Monday, Northern Ireland reported a higher daily number of Covid hospital inpatients, at 342, than the previous 8 April peak, when the number hit 322.
The NIAS asked for patience on Monday evening.
"We will prioritise calls to provide the quickest response to the most seriously ill or injured," it said.
In a social media post, the Southern Health Trust said: "Please only attend if you need emergency treatment, non urgent cases will have a long wait time."
Altnagelvin Hospital in Londonderry has reached a point where its critical care surge plan has been triggered.
In a statement, the Western Trust confirmed: "As numbers increase, we increase capacity as per our critical care surge plan up to 18 beds."
Meanwhile, there has been a outbreak of Covid cases in a ward at the Ulster Hospital.
Staff and patients test positive
Two patients and seven staff members in its coronary care ward have tested positive for Covid-19 at the hospital in Dundonald, the South Eastern Trust confirmed.
Nine other patients in ward 16 are self isolating and the ward has been closed to further admissions and visitors.
The South Eastern Trust said staff members who have tested positive for the virus are self-isolating at home.
It added that additional measures are in place to limit further spread.
"We would like to reassure all patients and members of the public attending the Ulster Hospital that it is safe to do so," the South Eastern Trust said, in a statement.
"Relatives of patients in ward 16 should contact the ward directly if they have any queries."
The Department of Health in Northern Ireland reported five further Covid-19 related deaths on Monday, bringing its total to 658.
There were 727 further positive cases, with the total number of cases now 34,832.
Three further deaths were recorded in the Republic of Ireland on Monday, with 939 newly confirmed cases of the virus.