At least 345 Muslims have died in this year's Hajj pilgrimage despite Saudi Arabia's attempts to prevent stampedes.
Saudi Arabia has spent millions to make the ceremony safer
Saudi authorities have spent millions of dollars since 2004 to improve safety measures on the Jamarat Bridge at Mina.
However, a British engineer who worked on the modifications said only a major redesign would reduce the risks.
Dr Keith Still described the Eastern Entrance as a "pinch point" to the whole system - one million people trying to get through a 45-metre gap.
More than two million Muslims flock to the Jamarat Bridge to hurl stones at pillars representing the spot where they believe the devil appeared to Abraham.
The Saudi interior ministry had promised a "special plan" to ensure a smooth flow of pilgrims towards the pillars.
Saudi troops patrolled the area, monitoring crowds, and helicopters flew overhead.
Dr Still told the BBC News website: "The Eastern Entrance at noon on the 12th day is a critical crush point. As soon as prayers are finished on the last day all the pilgrims want to get home.
"Even with 60,000 security forces in place, preventing more than one million Hajjis heading to that point is the irresistible force meeting the immoveable object. It's an impossible task."
In 2004, 251 pilgrims were trampled to death performing the ceremony.
New footbridges with emergency exits were built and three new pillars were erected that were wider and taller than ones used previously, so more pilgrims could pelt rocks at the same time.
Dr Still, who worked on the safety modifications, said the problems of the Eastern Entrance were highlighted to the Saudi authorities a number of times.
"The bridge is in the middle of a tight valley. Three major roads converge at the Eastern Entrance and there are 186 minor access routes to the area," he said.
The crowd flow is also impeded to the north by huge numbers of unregistered pilgrims squatting in the street with their baggage and tents, Dr Still said.
"Work on a new multiple-level design was due to begin as soon as this year's Hajj was over, giving access from the mountainside not just ground level.
"This is a terrible, terrible tragedy," he said.
Every able-bodied adult Muslim who can afford to make the trip is obliged to perform the Hajj, one of the five pillars of Islam, once in their lives.