Despite relatively mild weather and low levels of winter viruses such as flu, departments in major hospitals across the country ran out of space.
The country's newest acute hospital, the Forth Valley Royal in Larbert, started the week with 98% of beds occupied.
Aberdeen Royal Infirmary had 12 beds free on Monday morning - less than 2%. Edinburgh Royal Infirmary, the Victoria in Fife, Ayr Hospital and Crosshouse Hospital in Kilmarnock all began the week with 96.8% or more beds taken.
The Herald conducted the survey as part of the newspaper's NHS: Time for Action campaign, which is calling for a review of hospital and social care capacity to ensure services can cope with the growing elderly population.
While NHS Greater Glasgow and Clyde reported more than 300 beds were empty on Monday morning, 105 patients were being treated in the wrong department for their condition - a practice known as boarding.
Eight health boards were using boarding at the start of this week, with two boarders in Forth Valley, 42 in Lanarkshire, 42 in the Lothians and 41 in Ayrshire and Arran. The total number was 256. Grampian, Borders and Highland did not provide figures.
The Herald revealed more than 500 patients were boarding in Scottish hospitals on one day alone last winter.
Dr Neil Dewhurst, president of the Royal College of Physicians of Edinburgh, said: "These latest figures would suggest that the levels of boarding and bed capacity in some Scottish hospitals remain worryingly, and unacceptably, high. They also provide further evidence of the extent to which the discredited practice of boarding has become the norm in our hospitals.
"It is of particular concern that we have experienced a relatively mild winter so far, with limited reports of outbreaks of infection. If we are honest, we have been lucky. Increases in the number of cases of flu or norovirus could change the picture dramatically and put severe pressure on hospital services which in some areas are already operating beyond capacity."
Heather Knox, director of acute services for NHS Fife, said the board had encountered difficulties with discharging patients. She said: "Comparatively our patient numbers are similar to those experienced in the past few weeks. However, there has been an increase in the number of patients presenting with complex illnesses.
"The number of discharges is also down, leading to an increased number of patients in delay within hospital beds. This is due to difficulties the social work team is having in providing the required number of home care packages to secure discharge and maintain flow."
Clinicians are reporting that hospitals are coping better this winter compared to last year, when hundreds of people waited for hours on trolleys because of a shortage of ward beds.
This is partially due to extra investment and better planning but may also reflect less illness in the community.
A Scottish Government spokeswoman said: "The Scottish Government, working with the Royal College of Physicians of Edinburgh, is leading the way within the UK,in tackling the problems associated with boarding and patient flow.
"While on average NHS boards have coped better this year so far with winter, we recognise that peaks in demand may require use of beds flexibly at times.
"However, we are keen to ensure that NHS boards are managing their capacity and ensuring that for the majority of patients they are admitted to the right beds at the right time with the right staff."