Meinke and his wife, the artist Jeanne Clark, have lived in St. Petersburg, Florida since 1966. For 27 years, Meinke was a professor at Eckerd College, where he was a director of the EC Writing Workshop. In February 2004, he was inducted as a foundation member into the Eckerd College Phi Beta Kappa chapter, Zeta of Florida. He also served on the faculty of the Eckerd College's Third Annual Writers in Paradise Conference in January 2007. From 2003 through 2005, he held the Darden Chair in Creative Writing at Old Dominion University.

Meinke's published books include:

• Unheard Music: Stories (2007)
• The Contracted World: New & More Selected Poems (2006)
• Zinc Fingers: Poems A to Z (2000)
• The Shape of Poetry: A Practical Guide to Writing Poetry (1999)
• Scars (1945_
• Campocorto (Sow's ear) (1996)
• The Piano Tuner: Stories (1994)
• Liquid Paper (1992)
• Far from Home (1988)
• Underneath the Lantern (1986)
• Night Watch on the Chesapeake (1987)
• Trying to Surprise God (1981)
• The Rat Poems: Or, Rats Live On No Evil Star (1978)
• The Night Train & The Golden Bird (1977)
• Lines from Neuchatel (1974)
• Howard Nemerov (1968)
• The Legend of Larry, the Lizard (1968)