In 1998, Wheeler was elected a member of the National Academy of Engineering for "the computer simulation of subsurface flow and the underlying mathematical algorithms".
[2] In 2009 she was awarded the Theodore von Kármán Prize by the Society for Industrial and Applied Mathematics (SIAM).
[4] Wheeler studies finite element analysis and porous media problems with applications in engineering, oil-field exploitation, and the cleaning up of environmental pollution.
[4] She also studies environmental problems such as cleaning up underground reservoirs, spills of toxic waste, and carbon dioxide sequestration.
[4] In 1995 she moved to the University of Texas at Austin where she serves as the director of the Center for Subsurface Modeling at the Oden Institute for Computational Engineering and Sciences.