The three victims, two 28-year-olds a 27-year-old, were rushed to hospital following the attack at around 12.10am on Saturday morning on Old Shettleston Road, Shettleston.
They had stepped outside a house for a smoke when they saw two men trying to get into a close across the road. Following an argument the two men stabbed the three men causing serious injuries before running west down Old Shettleston Road .
One of the 28-year-old victims suffered a collapsed lung and the other 28-year-old suffered injuries to his groin and back.
The 27-year-old suffered stab wounds to his abdomen and arm.
All three men were taken to the Glasgow Royal Infirmary, where at two of them, the first 28-year-old and the 27-year-old, remain for treatment.
The condition of both men is described as serious but stable.
Police have appealed for information. The attackers are described as white, Scottish and aged between 18 and 25.
The first was 5ft 11ins, with broad shoulders, and was wearing a blue hoodie with the hood up and black tracksuit bottoms. The second is described as 5ft8ins, or medium build, and wearing black clothing.
Detective Sergeant Ross Jamieson from Shettleston CID, said: "This was a very nasty attack." Contact Shettleston CID with information on 101.