Props Martin, 20, and Hall, 19, have both extend their stays until the end of 2022.
Martin arrived last year having been honed in Leeds Rhinos' youth system.
He played nine times this season, scoring his first try for the club against Salford Red Devils.
Hall came through the Castleford academy system and made his debut in the win over Wigan Warriors last season.
He has made a further three appearances this term and Tigers coach Lee Radford said: "Sam has got a great skillset for a big bloke.
"Physically, he’s got what a lot of other young kids don’t and that’s his size.
"Hopefully we can nurture that skill and develop him into a big ball-playing middle.
“It is going to be a good opportunity to see what Brad is all about.
"He is going to get plenty of opportunities to develop and improve some of the good stuff he already does as a player.
“He’s a tough young bloke and I like the way he plays.”