[2] His first principal stage performance was in the musical Roberta at Her Majesty's Theatre, Melbourne, Australia in 1934.

[3][1] He made his New York debut as Captain Worthy in The Relapse, as part of the Theatre Guild (1950).

[7] Some of his best-known film and television roles include: In 1960 Matheson appeared as Alexander on the TV western Laramie on the episode titled "Duel at Parkinson Town.

"[8] In 1960–61, he was cast as Geoffrey Carey in "The Archer's Ring" and as the High Priest in "The Perils of Penrose", respectively, on the ABC series, Adventures in Paradise, starring Gardner McKay.

[9] In 1961, he played the lead guest-starring role in the episode "A Rope for Charlie Munday" on another ABC adventure series, The Islanders, co-starring William Reynolds.