Henry Carpenter Smither (July 28, 1873 – July 13, 1930) was a United States Army officer and American football coach. He served as the head football coach at the United States Military Academy from 1906 to 1907, compiling a record of 7–2–1. Smither died on July 13, 1930, at the Olney sanitarium in Lawrenceville, Illinois, following two operations for appendicitis.