Howard Clair Eshelman was born an only child in Canton, Illinois to Ellis and Marie Eshelman. Eshelman taught at Lee Junior College in Jackson, KY where he met his wife Lola Dykes Eshelman. They had four children. He was a chemistry professor and the acting head of the chemistry department at the University of Southwestern Louisiana (now University of Louisiana at Lafayette).

After graduating from Canton High School in 1924, Eshelman obtained a bachelor’s degree in science from Knox College, then earned a master’s degree in science from the University of Illinois. He pursued a doctoral degree at the University of Chicago, but his studies were interrupted by the decision to return to Lafayette to take the position as head of the chemistry department. Eshelman undertook research related to particle accelerators and cyclotron at the University of Chicago; he also completed research at the University of Tennessee, and published a paper entitled “Extraction and Flame Spectrophotometric Determination of Nickel”. Eshelman was associated with many organizations including the American Chemical Society, Petroleum Association, National Science Foundation, and the Analytical Chemistry Division of ACS. Eshelman was honored with the inscription of his name on a Plaque of Honor in the National Chemistry Society building in Washington, DC.