Slurry tank tragedy: Rugby star Nevin Spence killed
Promising young star Spence, 22, played at centre for the club and was called up to the Ireland training squad for the Six Nations last year.
The other men who died in the accident at Hillsborough, Co Down, are believed to be his brother and his father.
A woman thought to be his sister is being treated in hospital.
Ambulance crews were called to the farm just after 18:00 BST on Saturday.
The sister went to the Royal Victoria Hospital in Belfast where she is recovering from the effects of fume inhalation.
Spence had established himself as a regular in the Ulster squad in recent seasons, playing 42 times.
The former Wallace High School player made his first appearance for Ulster against Ospreys in April 2010. He played for the Ulster Ravens against Munster A at Deramore on Friday.
The Northern Ireland Ambulance Service (NIAS) sent rapid response teams to the farm in Drumlough Road.
In a statement, the service said the Northern Ireland Fire and Rescue Service pulled four people from the slurry pit, three of whom were unconscious.
NIAS paramedics tried to resuscitate the three men but two died at the scene.
The third man initially responded to resuscitation and was taken to the nearby Lagan Valley Hospital in Lisburn, where he died a short time later.