Figures for the Greater Glasgow health board area show the number of emergency admissions for people aged over 75s went up from 28,000 in 2004 to 37,000 last year.
Across Scotland the increase was almost 35,000, to just below 150,000 last year.
The Scottish Conservatives highlighted the figures with a call to ensure the NHS is prepared for the challenges presented by an increasing number of elderly people.
The number of people aged over 75 is projected to rise further in the next decade and by 86% by 2037. Health bosses expect to see an increase in associated illnesses, such as dementia.
Jackson Carlaw, the Scottish Tories' health spokesman, said in a Scottish Parliament debate on the NHS that Scotland had to face up to the challenges now.
He said: "The fact people are living longer is to be welcomed, but this is going to bring an array of challenges.
"The Scottish Government should have started preparing for this years ago. Instead, the number of nurses has been cut, and we hear no end of horror stories about the experiences of elderly patients in hospital.
"A huge proportion of these patients will have dementia, but not enough nurses are trained to deal with that in the context of an acute hospital setting."
Neil Findlay, Labour's health spokesman, called for a review to ensure the service was prepared for the 21st century.
He said: "Our NHS needs to be staffed properly, it needs to be managed effectively and people need to have confidence in it.
"For the sake of our best-loved public service, I appeal to the Cabinet Secretary (Scottish Health Secretary Alex Neil) to initiate that review today.
"The reality is the NHS in Scotland, the staff who work in it are under pressure like never before."
Liberal Democrat MSP Jim Hume said that while there were concerns over aspects of the NHS, including pressure on staff, his party did not support Labour calls for a review.
Mr Neil said planning and integration of social care would improve delivery of health services for all ages and he dismissed the calls for a review.
He said: "We know the way forward. We also know the problems, we understand the problems and the challenges, and we know what needs to be done."
He proposed an amendment to the Labour motion stating mandatory workforce planning was continuing and health and social care integration will empower service planning and delivery.
MSPs voted 64-38 with 11 abstentions for Mr Neil's amendment on the SNP's NHS policies.