The two soldiers who died during a training exercise in the Brecon Beacons were serving with the Territorial Army, according to the BBC.
Defence sources suggested the personnel had "succumbed" to unusually hot weather conditions during the drills in Wales.
The TA is a British volunteer reserve force which recently announced plans to increase its manpower to 30,000.
Emotional tributes have been paid to a third army reserve soldier who died from injuries sustained during SAS selection training.
One of two Army reservists killed in a military exercise in the Brecon Beacons on Saturday has been named as Lance Corporal Craig Roberts.