Loosehead Allan, a 23-year-old Scotland international, has extended his stay until 2018 while Tongan tighthead Puafisi has committed until the end of next season.
Allan, who has made 26 appearances since joining from Edinburgh in 2014, said: “I’m really enjoying my rugby in Glasgow with the way we play. There’s a great set-up at the club and the atmosphere in the squad is good as well.
“Last year was a great first season, but I’m always looking to improve and I feel I can do that at the Warriors.
“Being named in the Scotland squad for the RBS 6 Nations was a huge honour and I want to build on that selection and try and get more caps.”
Tonga international Puafisi has been an ever-present since joining from Gloucester last summer.
The 27-year-old said: “I’ve settled well in Glasgow and was delighted to sign for another year at the Warriors.
“I’ve made some really good friends at the club and all the players look after me and keep me right. The set-up at the club is great and the standard of play is really high.
“My wife and son really enjoy life in Scotland, so I’m looking forward to the rest of the season to see what we can achieve as well as next year, too.”
Warriors head coach Gregor Townsend, who added to his front row earlier this month by signing New Zealander Jarrod Firth, said: “Alex has been working hard on his set-piece game to build on his outstanding ability in general play. He’s had international recognition and is currently training with the Scotland squad and we believe he will continue to develop in our environment.
“Sila integrated so quickly after the Rugby World Cup it was as if he’d been a Warrior for the past 10 years. His workrate in training and in games is excellent, and he has been really solid at scrum time.”