[2][3] He served as law clerk to Alexander Farrelly and Antonio L. Joseph of the Municipal Court of the Virgin Islands.

He served as a judge advocate in the U.S. Army in Vietnam from 1966 to 1969, first as a first lieutenant, then as a captain, earning a Bronze Star Medal.

[3] Finch was nominated to the District Court of the Virgin Islands by George H. W. Bush on June 19, 1992.

[4] On March 22, 1994, he was nominated to the same court by Bill Clinton, and he was confirmed by the United States Senate on May 6, 1994.

[3] As his 10-year term was expiring, Finch was renominated to the same court by George W. Bush on February 2, 2004, and was confirmed by the Senate on November 21, 2004.