Fung was born in Jiangsu Province, China in 1919. He earned a bachelors degree in 1941 and a masters degree in 1943 from the National Central University (later renamed Nanjing University in mainland China and reinstated in Taiwan), and earned a Ph.D. from the California Institute of Technology in 1948. Fung was Professor Emeritus and Research Engineer at the University of California San Diego. He published prominent texts along with Pin Tong who was then at Hong Kong University of Science & Technology. Fung died at the Jacobs Medical Center in San Diego, California, aged 100, on December 15, 2019.
Fung was married to Luna Yu Hsien-Shih, a former mathematician and cofounder of the UC San Diego International Center, until her death in 2017. The couple raised two children.