Neither will be available to practice when the Colts hold their first training camp practice Sunday.
Angerer is recovering from off-season surgery on his right foot after playing through the injury last season. Moala is trying to come back from surgery on his right knee, an injury that ended his 2012 season in November.
They join running back Ahmad Bradshaw on PUP. The former New York Giants running back had off-season surgery on his right foot in January. The unrestricted free agent signed with Indy in June.
Angerer, Indy's second-round draft pick in 2010, has 278 career tackles. Moala has 86 tackles since the Colts drafted him in 2009.