Anthony David Mounce (born February 8, 1975) is a former Major League Baseball pitcher. He pitched in 11 games (starting all 11) for the Texas Rangers in 2003, winning 1 and losing 5. Mounce was originally selected by the Houston Astros in the 7th round of the 1994 Major League Baseball draft. Over the next five seasons, he worked his way up to the Astros' farm system as a starting pitcher. In 1999, after having been converted into a relief pitcher, he made it to their Class AAA team, the New Orleans Zephyrs. He pitched 14 games (11 innings) with a 2.45 ERA, but was released by the Astros at the end of spring training, 2000.