New figures revealed that of a total of 1500 vacancies for nurses and midwives, more than 350 had still not been filled after 12 weeks.
The statistics from ISD Scotland, the health service's information body, found NHS Greater Glasgow and Clyde and NHS Grampian had the highest number of long-term nursing vacancies in December last year.
Across Scotland, most of the 352 NHS posts which had been empty for three months were in the area of adult nursing, while there were 30 long-term nursing vacancies in the mental health field.
The Herald has been camp-aigning on the issue of whether Scottish hospitals have enough beds and staff to cope with the rising number of elderly patients.
The Scottish Conservatives, who obtained the figures, said the large number of vacancies was due to cuts to student nurse fund-ing in 2012, and a retirement boom among the nursing workforce, more than a third of whom are over 50.
Jackson Carlaw MSP, the party's health spokesman said: "The Scottish Government has planned disastrously on the nursing front. They cut the number of student nurses without thinking about challenges coming down the track.
"The fact there are hundreds of vacancies lying unfilled for so long is a damning indictment on the way the SNP has run the NHS.
"We recognise the challenges an ageing population will bring, and the reality of how overworked nurses currently are."
He added that the Scottish Conservatives had pledged to bring in 1000 extra nurses to cope with this pressure, by scrapping free prescriptions for those who could afford to pay.
Margaret Watt, chairwoman of Scotland's Patients' Association, said: "This is a real concern. Nurses and midwives are overworked as it is and if vacancies aren't being filled it inevitably puts more strain on those who remain.
"Sick people and women who have just had babies need and deserve proper attention and if nurses and midwives are really stretched, the level of care being given is compromised. I believe they just can't care for the patients the way they would like to as they are so busy and so stressed out."
Last month the Royal College of Nursing Scotland said a shortage of qualified nurses was putting pressure on health boards trying to recruit more staff.
Ellen Hudson, RCN Scotland associate director, said at the time: "Demand is going up as people live longer, often with a range of complicated conditions. So while health boards are putting right past cuts and trying to recruit nurses to try to meet this demand, pressure is still growing because health boards are trying to recruit to posts but there aren't enough appropriately qualified nurses."
A Scottish Government spokesman said ministers had recently announced a 4% rise in student intake numbers from 2430 in academic year 2012-13 to 2530 in 2013-14 and that the number of full- time nurses and midwives in the NHS in Scotland had risen by 2.7% under the current government.
He said there are more qualified nurses and midwives per 1000 population in NHS Scotland than in NHS England with a ratio of 7.9 staff in Scotland per 1000 compared to 5.8 in England.
He added: "The NHS workforce has grown by more than 2300 in the last year alone. Under this Government, we have over 2400 more nurses and medical staff in post. In the last year alone there has been an increase of 1000 extra nurses, and over 250 more medical staff."