He appeared on Broadway, but is best known for his supporting roles in several films and television series.
Sheiner appeared in several films including The Greatest Story Ever Told (1965) as James the Elder, They Call Me Mister Tibbs!
He is probably best known for his supporting role as Roy, Oscar's accountant and poker playing crony opposite Jack Lemmon and Walter Matthau in the film adaptation of The Odd Couple (1968).
Sheiner also featured prominently in the 1973 Michael Winner/Charles Bronson action movie "The Stone Killer".
He also played roles on several other popular shows such as Columbo, The Big Valley, The Twilight Zone, The Invaders, Voyage to the Bottom of the Sea, The Man from U.N.C.L.E., Cannon, Hawaii Five-O, Blue Light, S.W.A.T., Quincy, M.E., Mission: Impossible, The Fall Guy, Vega$, Blind Ambition, Planet of the Apes, Bonanza, and The Fugitive.