Cummings and Brown have not featured in this season's tournament due to injury.
Brown has 54 caps but missed both the Six Nations and Autumn Nations Series in 2021 through injury.
Cummings recovered from hand surgery in time to start the final November Test against Japan but has not featured for Scotland since then.
His return from a knee issue adds competition to a second row pool that is once again missing Jonny Gray, who has an ankle injury.
Gregor Townsend has also called up two relatively unknown players in uncapped duo Walker and Jordan Edmunds.
Walker is a 22-year-old tighthead prop with Glasgow while Edmunds, 25, is a winger from Edinburgh who is a regular in the Scotland Sevens squad.
Winger Duhan van der Merwe remains suspended after a ban for reckless play for Worcester resulted in him sitting out Saturday's win in Italy.
Uncapped forwards Kiran McDonald and Glen Young have been released from the squad to return to Glasgow and Edinburgh respectively.