The dead soldiers were named as corporals Robert Hawksley, 29, from Nottinghamshire, and Martin Bailey, 25, from Northamptonshire. They were serving with the Queen's Royal Lancers, based at Osnabruck, Germany. Both were single.
It was the second tragedy to hit the British training unit in a week. Last Thursday another soldier was killed when his Land Rover collided with a 13-ton armoured personnel carrier.
The Army said a board of inquiry would be set up to establish the cause of the latest accident.
The British Army Training Unit at Suffield, Alberta, has been operational since 1972 and provides the Army with its only peacetime opportunity to practise fire and movement with a whole battle group across the prairie.
Initial reports indicate that the soldiers were buried alive in a collapsed trench which, sources said, could have been caused by an artillery impact or by an earth tremor.
Last night the Army refused to divulge the exact composition of the battle group to which the dead soldiers belonged.
'Like anything in war, it's a risky business', a Ministry of Defence spokesman said.