NHS Lanarkshire said the number of people who needed treatment and ward beds had been particularly high during July and August.
Extra doctors and nurses have been drafted to help the three hospitals in the region to cope.
The picture of pressure in Lanarkshire emerged after news patients had to queue on trolleys for beds in Glasgow's Western Infirmary this week. Clinicians described demand for beds in the city's hospitals as similar to the winter months, when viruses such as flu tend to circulate.
While health boards in other parts of Scotland such as NHS Tayside and NHS Grampian said their accident and emergency departments were no busier than usual, figures from Borders General showed the number of patients arriving at A&E rose 11 per cent during June and July compared to last year.
NHS Forth Valley also said it had experienced "some pressures" in recent weeks, although patients have not had to wait on trolleys at Forth Valley Royal Hospital in Larbert. NHS Borders said it was still treating 95 per cent of patients within the Scottish Government's four-hour target.
Hairymyres, Monklands and Wishaw General hospitals in Lanarkshire have seen 14,118 patients in emergency departments so far this August.
A spokeswoman for NHS Lanarkshire said: "NHS Lanarkshire has experienced particularly high levels of A&E attendances and associated emergency admissions, comparable to winter numbers, throughout both July and August. This has especially been the case within the last week. There has been increased pressure on bed availability within all three acute hospitals in Lanarkshire."
The board said various actions were being taken to improve the flow of patients through the hospital. It is currently advertising for nine consultants in emergency medicine and a further advert for nine physicians is due to run next month. However, there is currently a UK-wide shortage of people wanting to specialise in emergency and acute medicine.
Scottish Labour health spokesman Neil Findlay said the SNP government need to act now and "undertake a comprehensive review of our NHS to ensure that it is fit for purpose."
A Scottish Government spokesman said: "Long waits in A&E are unacceptable, which is why we're working with boards to invest £50 million through the unscheduled care action plan."
l Hundreds of children and young people in Scotland with mental health problems are waiting more than six months to see a psychiatrist.
At the end of June, 5300 people were still waiting to start specialist treatment at child and adolescent mental health service services, according to recent figures.