Junior outfielders Lauren Bauer and Nicole Giordano and junior third baseman Toni Mascarenas earned second-team honors in the voting conducted by a National Fastpitch Coaches Association committee.
Junior catcher Lindsey Collins was named to the NFCA All-America third team.
Arizona has had five or more players honored as All-Americans eight times since 1992, the year after the Cats won their first of five NCAA Championships.
"It's a nice honor and our players certainly were deserving, but I wish they'd hold the ceremony at some other time of the year," Arizona coach Mike Candrea said. He and the Wildcats are in town preparing for the 19th annual Women's College World Series, for which the UA is the No. 2 seed after a 13th consecutive NCAA Regional championship last week.
"This is a time for each of the eight teams to be honored for their accomplishments in having good seasons and getting to the World Series. I want our players thinking about that. The individual stuff would be better cited later in the year, such as at the NFCA convention," he said.
Finch, was Most Outstanding Player in NCAA Region 2 action in Tucson last weekend, and joined on the All-Tournament team by each of the Cats who received All-America honors, along with teammates Becky Lemke, a junior pitcher, and senior second baseman Katie Swan.
Bauer and Giordano, third-team All-America picks in 1999, earned repeat honors, as did Mascarenas, who along with Bauer was a first-team selection in 1998 following their freshman seasons. Finch, Mascarenas, Collins and Giordano earned first-team All-Pacific Region honors last weekend, while Bauer was a second-team selection.