* Theodore von Karman Medal, 1976
* Otto Laporte Award, 1977
* Worcester Reed Warner Medal, 1984
* Jean-Leonard-Marie Poiseuille Award, 1986
* Timoshenko Medal, 1991
* Lissner Award for Bioengineering, from ASME
* Borelli Medal, from ASB
* Landis Award, from Microcirculation Society
* Alza Award, from BMES
* Melville Medal, 1994
* United States National Academy of Engineering Founders Award (NAE Founders Award), 1998
* National Medal of Science, 2000
* Fritz J. and Dolores H. Russ Prize, 2007 ("for the characterization and modeling of human tissue mechanics and function leading to prevention and mitigation of trauma.")
* Revelle Medal, from UC San Diego, 2016
Fung was elected to the United States National Academy of Sciences (1993), the National Academy of Engineering (1979), the Institute of Medicine (1991), the Academia Sinica (1968), and was a Foreign Member of the Chinese Academy of Sciences (1994 election).