Experts are speculating that the crash was caused by a catastrophic situation, rather than a mechanical fault.
Unconfirmed reports have claimed to have seen some sort of explosion in the night sky around the time the flight went down.
Egyptair have confirmed a distress call was made by the plane before it went missing.
The flight was 280km from Egytian coast when it went missing.
The captain on the flight had 6,000 hours experience.
Egypt are currently searching for the plane with help from Greece.
Ihab Raslan, a spokesman for the Egyptian civil aviation authority, said the plane was about to enter Egyptian airspace when it disappeared from radar. The airline, however, said the Airbus A320 had vanished 10 miles after it entered Egyptian airspace.
Around 15 family members of passengers on board the missing flight arrived at Cairo airport and authorities brought doctors to the scene after several collapsed.
EgyptAir Flight 804 was lost from radar at 2.45am local time when it was flying at 37,000 feet, the airline said.
Egyptian aviation officials say they believe a missing plane – with 66 people on board – has crashed into the Mediterranean Sea.
Sky’s Sharine Tadros says Egyptair has released the nationalities of those on board: “Many different nationalities including 30 Egyptians, 15 French nationals, one British national, One Belgium national, two from Iraq and then various other countries.
“We are just going down the list, from Saudi Arabia, from Chad, from Sudan.”
A flight from Paris to Cairo, flight number MS804 has disappeared from radar screens above the Mediterranean.
Egyptair has said there were 56 passengers on board – including a child and two babies.
The plane also had a crew of 10.
The flight, from Paris CDG, disappeared while flying at an altitude of 37,000ft after entering Egyptian airspace.
There is no indication as of yet of distress calls or mechanical trouble and there are no reports of bad weather.
A search and rescue mission is now ongoing.