Some acute heart patients are waiting weeks in hospital for an operation, too sick to go home but unable to get a surgical slot.
And brain and cancer surgeries are also being delayed as the winter pressure on hospitals extends to intensive care.
Most hospitals said they had been delaying non-urgent surgery because wards were so full or too many staff were sick.
But Cardiac Society chairperson and cardiologist Selwyn Wong said patients needing urgent procedures were now waiting much longer than normal.
They may have had heart attacks or a type of heart failure but were waiting up to three weeks for their surgery.
"These are people deemed sick enough to wait in hospital and not safe enough to be waiting at home for their operations," he said.
"The ones that are very urgent will get done first and the ones that are urgent will wait longer than we would hope."
There was a risk they would get worse waiting, he said.
Part of the problem was the pressure on intensive care units, which were becoming clogged with patients and facing staff shortages.
Many heart patients needed an intensive care bed after their surgery, but there was often not one available.
An intensive care specialist and Intensive Care Society spokesperson Andrew Stapleton said it was the same for several other serious conditions, including some brain surgery and tricky cancer operations, like for liver cancer.
With many hospitals very full, there were sometimes no ward beds available to move patients to when they were deemed well enough to leave the ICU - a situation known as exit block.
That meant they had to stay in the ICU longer, preventing space being freed up for new patients.
Sometimes, those who needed intensive care got it by being moved to another part of the country, something that had been a protocol long before Covid-19 pressures, he said.
"It's like a gianantic game of chess being played at all times."
Winter illnesses were hitting ICU workers too.
In some units, senior doctors were having to step in to fill in in junior doctor roles, he said.
Dr Stapleton said it was encouraging to see Covid-19 cases reducing, but said there was likely to be pressure on intensive care wards for a few weeks yet.
Dr Wong said short staffing among other parts of the hospital, like theatre nurses, was also contributing to the surgical delays.
His colleagues were making good decisions about who should be prioritised, but it was very frustrating to see people who really needed surgery having to wait longer than they should, he said.
Dr Wong told Morning Report the hospital system was not just under pressure, "it is strained".
Te Whatu Ora, the new national health authority, said there was intensive care capacity this week, with about 72 percent of intensive care or high dependency beds in use on Tuesday.
ICUs and HDUs had been busy but still had capacity to handle critical patients, a spokesperson said.
Hospitals were delivering as much planned care as possible, and triaging those with the highest clinical need, they said.
Dr Stapleton said delays to planned care were allowing more capacity, but it was very difficult to measure because it could change from shift to shift - especially with staffing levels.
Some areas of the country were worse affected that others, he said.
There was some hope for intensive care in the medium term, with work already underway to spend new funding to create 84 more beds nationwide, he said.
Dr Stapleton told Morning Report that public health measures were the only thing that could really make a difference in the next few weeks.
People were not being as diligent about mask-wearing and isolating as they should be, he said, because they don't perceive the threat of the illness as bad.
This had knock-on effects for hospitals, he said.
"Our message would be please wear masks if you can, it's not really much of an imposition, and make sure you stay home if you're sick and isolate..."