Two of the victims, both in their twenties, are in serious condition in hospital as a result of the "very nasty" assault in the early hours of Saturday.
The attack, in the Shettleston area of Glasgow, is being treated as attempted murder by police.
The trio, two aged 28 and one aged 27, were standing smoking outside a close in Old Shettleston Road at around 12.10am when they became involved in a row with two men trying to get access to another nearby close.
A short time later the two suspects crossed the road and attacked all three men and fled west on Old Shettleston Road.
The victims were taken to the city's Royal Infirmary with serious stab wounds.
One of the 28-year-olds suffered a collapsed lung and is in a serious condition. The 27-year-old man suffered stabs wounds to his abdomen and arm. He is also in a serious condition in hospital.
The other 28-year-old man suffered injuries to his groin and back but has been released from hospital.
Detectives are asking anyone with information about the attack to come forward.
The two attackers are said to be white, Scottish and aged between 18 and 25.
One is 5ft 11in, with broad shoulders and was wearing a blue hooded top, with the hood up, and black tracksuit bottoms.
The other attacker is around 5ft 8in and of medium build, wearing all black clothing.
Detective Sergeant Ross Jamieson, of Shettleston CID, said: "This was a very nasty attack. The men had been outside in a close for a smoke when for whatever reason they became involved in a shouting match with two men across the road which resulted in all three being viciously stabbed.
"Although it happened in the early hours of the morning, this is a busy road and surrounded by flats and it is quite possible that someone saw or heard this attack take place."
Shettleston CID can be contacted by ringing 101.