Bevan and Bichel, both 33, missed out as selectors moved to revamp their playing roster in the post-Waugh era by awarding South Australian quick Shaun Tait and Victoria's Brad Hodge their first contracts.
Nathan Bracken, Ashley Noffke and Nathan Hauritz were also dropped from the list of 25 contracted players, which forms the pool from which most of the Australian Test and One-day squads are drawn.
Australia has dominated world cricket in recent years under the leadership of Steve Waugh, but his departure earlier this year and the advancing age of some of its superstars has dented its intimidating aura.
The list of 25 contracted players includes 14 aged over 30 and only three aged under 25.
Chairman of selectors Trevor Hohns said Cricket Australia was seeking a blend of experience and "raw, emerging talent".
He praised the contribution of Bevan, once hailed as the world's best One-day batsman, but said selectors were looking to the future.
"It was felt that Michael's contribution to the One-day side has decreased and, importantly, we thought it was the right time to move forward as we start to form a core group of players to take us to the next World Cup," he said.
Bevan averaged 53.58 in 196 One-day innings but never cut the same dash in Tests, averaging 29.07 in 30 innings in the long form of the game, the last played in 1997/98 against South Africa.
He was part of Australia's victorious World Cup sides in 1999 and 2003.
Bichel, also part of the 2003 World Cup squad, was regarded as an honest toiler who relished his every international appearance after making his debut aged 26.
Hohns said selectors had showed their hand when they dropped Bichel from the Test and One-day sides during the summer.
Victorian batsman Matthew Elliott was awarded his first contract since the 2000-2001 season while West Australian Michael Hussey returned to the list after a two-year absence.