Lock Wykes has made 53 appearances for the club since making his debut in 2009, while experienced prop Faulker has appeared 11 times for the Australian outfit.
Head coach Michael Foley told reporters at a press conference: "It's further endorsement for what we're looking to achieve as a team to have guys like Sam and Tetera re-commit to the club.
"Sam's returned to the field following a knee reconstruction last year; he's responded to the extra responsibility he's taken on within the team and will continue to develop as a leader into the future.
"While still relatively young for a prop, Tetera has shown good development as a two-sided prop, and will continue to be an asset to the side moving forward."
Neither Wykes nor Faulkner has gained full recognition for Australia.