The hearing takes place at the Commando Training Centre at Lympstone, near Exmouth, Devon, and is expected to last several days.
Prince Edward was the most famous cadet ever to fail the Commando tough training course there - which recruits must pass to win the coveted green beret. The course includes endurance and assault courses, and "yomps" with full kit across Dartmoor.
The court martial follows an investigation launched after half a dozen recruits made allegations against the training staff in late 1996.
A lieutenant and two non-commissioned officers - a troop sergeant and a corporal - face charges. The sergeant faces five charges of allegedly ill-treating soldiers, and the corporal one charge. The lieutenant faces a charge of improper behaviour in allegedly failing to report the bullying.