Dr Adrian Harrop, an A&E doctor at Scarborough Hospital, took to Twitter to reveal what the "broken and underfunded system looks like".
York Teaching Hospital NHS Foundation Trust, which runs Scarborough and Bridlington Hospital, has said cases for cancelling operations are being reviewed on an individual basis.
But the pressures on Scarborough's accident and emergency department are rapidly increasing.
Patients have been waiting up to nine hours to see a doctor and many have spent hours on trolleys as the number of beds available plummet.
On January 3, Dr Harrop claimed the last available space had gone. He said: "I have no more capacity to offer, even to the sickest of the sick patients. This is unsafe."
He later tweeted: "We are now at the stage of declaring a major incident. We are no longer able to offer safe of adequate care to the patients in our hospital.
"This is a critical and unmanageable situation, and the plan as it stands at the moment is not working. This is a crisis."
A major incident was declared three years ago at Scarborough Hospital in January 2015 because of an unexpectedly high demand for its services.
But the trust has denied that it is currently at a stage where it needs to declare a major incident.
A spokesperson for York Teaching Hospital NHS Foundation Trust said: “Like all hospitals across the country, Scarborough Hospital has been exceptionally busy over recent weeks with a high number of emergency attendances and a lot of very ill patients.
"The hospital is currently coping well under very difficult circumstances and we would like to thank our staff for their continued hard work and commitment to our patients under intense pressure.
“Patient safety remains our top priority. Patients are treated according to clinical need, and those requiring urgent attention are seen promptly, however when we are facing high demand those with minor or less urgent needs may find that they are waiting longer.
“We have been urging people to only come to the Emergency Department in an emergency situation. This will ensure that we can dedicate our resources to the most acutely ill patients.”
Across the UK, non-urgent treatments have already been cancelled until mid-January, but NHS England said on Tuesday that this would now be extended to the end of the month.
The trust says operations and appointments at Scarborough are being reviewed on an individual basis and only those operations that can be safely deferred to a later date will be rearranged.