The shootings happened in the Glenveagh Drive area of the city on Thursday.
The men, aged 25, 24 and 18, were each shot twice in the legs at around 10.30pm.
They were taken to hospital for treatment to their injuries, which are not believed to be life-threatening.
Police are appealing for information about the attack, and a spokesman added: "The motive for the shooting is still being investigated at this stage."
Tim Attwood is SDLP councillor for the area. He described the shooting as a very serious incident.
He said: "Nobody has given these thugs the right to be judge, jury and enforcer in our communities.
"We have a fully accountable policing service, let the PSNI to their job and allow due process and justice to prevail."
Sinn Féin MP Paul Maskey has called for those who carried out the shooting to leave the people of the area alone.
The west Belfast representative said: "It is well documented that the gangs responsible for these types of attacks are heavily involved in criminality themselves.
"They offer the community nothing but misery and the people can see through their hypocrisy of claiming to be helping the community.
"These gangs will not stop this community from moving forward and the sooner they get the message that they are not wanted, the better."