Michael J. Shelley (born August 17, 1959) is an American applied mathematician who works on the modeling and simulation of complex systems arising in physics and biology. This has included free-boundary problems in fluids and materials science, singularity formation in partial differential equations, modeling visual perception in the primary visual cortex, dynamics of complex and active fluids, cellular biophysics, and fluid-structure interaction problems such as the flapping of flags, stream-lining in nature, and flapping flight. He is also the co-founder and co-director of the Courant Institute's Applied Mathematics Lab.