Professor Elson graduated from Harvard University in 1959 with an A.B. in Biochemical Science. His graduate work at Stanford University (Ph.D., 1966) was with Robert Baldwin in the Department of Biochemistry. After a post-doc with Bruno Zimm at the University of California San Diego, he joined the chemistry faculty of Cornell University in 1968 as an Assistant Professor. He was promoted to Associate Professor in 1974 and Professor in 1978.

At Cornell he pioneered the development of fluorescence correlation spectroscopy and fluorescence photobleaching recovery in collaboration with Watt Webb of the Cornell Physics Department, and also developed the repetitive pressure perturbation kinetics method. In 1979 he moved to the Department of Biological Chemistry (now the Department of Biochemistry and Molecular Biophysics) at Washington University School of Medicine, where he has studied the movement and distribution of cell surface proteins, cell motility, and the forces which determine the shapes of cells.