At least one has no spare beds while another entire region said it is nearing 100 per cent capacity.
The number of people in hospital with coronavirus is now higher than during the peak of the first wave last April.
At University Hospital Wishaw, in Lanarkshire, there are no beds available.
NHS Lanarkshire is dealing with more coronavirus patients than at any point since the pandemic began.
As of 8am on Monday, 288 patients were being treated for the virus in its hospitals, including 103 in Wishaw. Coronavirus cases account for almost a quarter of the hospital’s 420 beds.
Across NHS Lanarkshire on Monday, hospitals were running at 96 per cent capacity with just 46 free beds in the whole of the health board area for new patients.
Last night the board decided to temporarily postpone all non-urgent elective procedures and a targeted range of outpatient appointments from today to help ease the burden.
NHS Lanarkshire said it would focus on acute service delivery for Covid inpatients and emergency care.
Treatments for urgent cancer care will remain and the board will continue to operate an emergency service for theatres and diagnostics.
The majority of outpatient appointments will be stood down to allow nurses to support delivery of urgent and emergency inpatient care.
The measures will last for four weeks but may be extended.
They come amid fears the numbers of Covid patients will double within seven days from the current figure of 288, with 16 in intensive care.
Judith Park, director of acute services for NHS Lanarkshire, said: “We currently have nearly 300 patients being treated for Covid-19 in our hospitals, with additional patients currently waiting on test results.
“However, we are anticipating this number to double within a week, putting our hospitals under severe pressure.”
In Dumfries and Galloway, the health board says its hospitals are nearly full.
A spokesman said: “We currently have 48 Covid-positive patients in hospital – the highest number during the course of the pandemic.
“We are close to 100 per cent capacity but are managing this situation with contingency plans to increase capacity if it is required.”
NHS Dumfries and Galloway CEO Jeff Ace said the area’s luck has “run out” as they have seen a massive surge in Covid cases fuelled by the new variant strain pushing emergency services close to breaking point.
The rapid rise in cases, which are increasing by about 100 a day, has left the NHS struggling to maintain services in the accident and emergency department.
Ace revealed the “frankly grim picture” in a Twitter video. He said there was a “real concern about whether we can keep accident and emergency services running safely and effectively”.
In Ayrshire & Arran, where First Minister Nicola Sturgeon recently reported hospitals were at 96 per cent capacity, Ayr Hospital could only manage to see 81.6 per cent of patients in the time frame and Crosshouse Hospital, near Kilmarnock, was worse at just 72.7 per cent.
NHS Ayrshire & Arran medical director Dr Crawford McGuffie said: “This phase of the pandemic is having the greatest impact on our
communities in terms of positive cases, numbers admitted to hospital and, sadly, deaths.
“It is placing great strain on every aspect of the system.
“This includes care workers, care homes, district nurses and GPs supporting vulnerable citizens at home and in the community, as well as emergency departments, admission units, wards and intensive care units within the hospitals.
“Despite the measures in place, there have been outbreaks of Covid-19 in the lower-risk areas among patients and staff.
“This has, at times, resulted in wards closing to new admissions, which means additional beds cannot be used for a short period of time.”
Aberdeen Royal Infirmary reported being at 75.9 per cent capacity while Borders General Hospital and Edinburgh Royal Infirmary were marginally better on 76.9 and 79.5 per cent.
Park added: “We are currently dealing with a high number of Covid-19 patients across our hospitals which continues to cause severe pressure on our resources.
“A number of wards are currently closed to new admissions and transfers.
“Strict control measures are in place to reduce the risk of infection. The safety of our patients and staff is of paramount importance and we continue to take all necessary action to ensure safe and effective patient care.”
NHS Grampian now have more Covid-19 patients in hospital than at any other point during the pandemic.
A spokeswoman said: “The health board has seen the number of Covid-19 positive patients in hospital surge by 160 per cent in less than three weeks – from 39 on Christmas Eve to about 100 today. During last year’s peak, the number of Covid-19 patients in north-east hospitals topped at 89.”
Jacquie Campbell, chief officer of acute services with NHS Lothian, said there was no doubt “our hospitals are under significant pressure”.
Last night Scottish Labour’s health spokeswoman Monica Lennon said: “Hospitals are reaching patient capacity with no let-up in sight, staff reaching breaking point and putting themselves at risk to deliver services.
“Covid cases are increasing and still the Government fails to act fast enough to equip our NHS hospitals to cope with an influx of patients.
“The announcement from NHS Lanarkshire is just the tip of the iceberg. Ministers must act now if we are to prevent further cuts to non-Covid hospital treatments.”