Educated at St Bede's College, Graf made his grade debut at the age of 19 for St Kilda Cricket Club in the 1976–77 season as an all-rounder, bowling right-arm medium fast and batting left-handed with an emphasis on driving.

Graf travelled to England during 1979 and played for Wilshire in the Minor Counties competition. Highlights include 51 against Oxfordshire, 7–73 against Dorset and 79 and four wickets against Berkshire. He took 6–27 playing for the Gloucestershire Second XI.

1979–80 First Class Debut

Graf made his first-class debut in 1979–80 for Victoria.

He turned in a number of notable performances that season, including 3–24 against WA, 58 not out against WA, and seven wickets against South Australia.

Graf also had some good games in the McDonald's Cup. In his debut he took 1–44 and 19 not out against SA, helping Victoria win by three wickets. In the final he took 2–34, helping Victoria win the game and the championship. Victoria also won the Sheffield Shield that season.

In grade cricket, Graf took 4–54 and scored 93 helping St Kilda beat Melbourne. He took five wickets in the final but Footscray won the match.

1980 – Hampshire

Graf received an offer to play over the 1980 English summer with the Hampshire County Cricket Club. He performed disappointingly, scoring 214 runs at 19 and only exceeding 50 in a first-class game once, and taking only 16 first-class wickets at an average of 48 with best figures of 2–24. Highlights included 44 against Oxford, Hampshire came last that season. and 57 not out against Essex in his final county game.

His form was slightly better in one day games, taking 3–44 against Derbyshire, 2–12 against Somerset, 3–26 against Lancashire, and 2–24 against Essex.

He also had some good games for the Hampshire 2nd XI, taking five wickets and scoring 51 in one game.

1980–81 – International Player

Graf's first-class form was better in the Australian 1980–81 season. In his first Shield game, against WA, he scored 34 and 64 and took four wickets. He leapt into international consideration in another game against WA, scoring 100 not out and taking 3–24. In one day games he took 2–6 against Queensland.

Australia was looking for an all rounder and these efforts saw Graf named in the Test team for the second Test against the touring New Zealand. Graf wound up as 12th man though and did not play.

He was however selected to make his ODI debut in November 1980 against New Zealand at the Adelaide Oval.

"If we have a deficiency at the moment, it is possibly that we lack a true all-rounder", said Australian captain Greg Chappell at the time. "Shaun Graf is an up-and-comer in this area and he is possibly what Australia needs – not only in one day cricket but in Test matches as well".

Graf made a duck and took 1/40 in the match. He was kept on in the side for the next game, against New Zealand, taking 2–40. Against India he took 0–30 and scored 5. He took 0–15 against New Zealand