Dr. Hughes is an elected member of the U.S. National Academy of Sciences, the U.S. National Academy of Engineering, the American Academy of Arts and Sciences, the Royal Society of London, the Austrian Academy of Sciences (Section for Mathematics and the Physical Sciences), the Istituto Lombardo Accademia di Scienze e Lettere (Mathematics Section), and the Academy of Medicine, Engineering and Science of Texas.

Dr. Hughes is a Fellow of the American Association for the Advancement of Science (AAAS), the American Institute of Aeronautics and Astronautics (AIAA), the American Society of Civil Engineers (ASCE), the American Society of Mechanical Engineers (ASME), the U.S. Association for Computational Mechanics (USACM), the International Association for Computational Mechanics (IACM), the American Academy of Mechanics (AAM), the Society for Industrial and Applied Mathematics (SIAM), and the Engineering Mechanics Institute of ASCE. He has been elected to Distinguished Membership in ASCE, the highest honor ASCE bestows.