It is believed the car park chaos is due to roadworks near the entrance to the car park on Swinegate.
Swinegate is down to one lane today (Sunday) and it is believed ongoing traffic towards the city centre is causing problems as cars leaving the car park are having to wait to join the lane of traffic.
The YEP can confirm that the cars were still backed up to the sixth floor at 5.30pm.
Lots of people turned their engines off, some people sat with their doors wide open and some abandoned their cars entirely.
People we spoke to were very frustrated and there was a number of cars beeping their horns out of anger.
One woman we spoke to as we entered the car park warned us "not to bother" trying to get a car out.
She said it was "chaos" and she and her friends had abandoned their car and gone back into town.
Another woman we spoke to on the stairs had to leave her car to fetch food for her baby.
She had been there over an hour.
She said: "No one knows what is going on or if we will have to pay extra. We've been told we can get an extra hour and a half but after that - we would have to pay.
"We have a baby in the car with us and she has been screaming. I've had to leave to get her something to eat and drink."
Mrs Fisher, 29, had been stuck on the sixth floor for more than an hour and has seen people abandon their cars out of frustration.
Mrs Fisher said: "There are hundreds of cars just at a standstill.
"Apparently it's because of roadworks at the bottom of the road but they should have been managed better. Someone needs to be accountable."
Joanne Moule, 50, from Leeds had left her car to try and find out what was happening.
She said: "We've been here hours. It's because they haven't stopped the oncoming traffic so it's all jammed at the bottom.
"They need to manage the road better and release 50 cars at a time - they have to keep the flow going.
"We saw it was busy but we didn't expect it to be like this. Nightmare."
Susan Nicholl, 40, from Halifax had just come shopping with her two children.
She and her children had been stuck in the car for an hour.
She said: "I bet we are probably going to be stuck here for another 3 hours."
Trinity Leeds has been contacted and no one was available for comment at this time.
Leeds Council has been contacted for comment.
Landsec has been contacted for comment.