Buckmire's research areas are computational aerodynamics, scientific computation, numerical analysis, mathematical modeling of physical situations, and applying mathematics to "real world" situations. He has published in a number of journals, including Numerical Methods for Partial Differential Equations, IMA Journal of Management Mathematics, Works and Days and the Albany Law Review. From 2011 to 2013 he served as a Program Director in the National Science Foundation's Division of Undergraduate Education.