The application of a mechanical field is seen to cause a switching of the director orientation in a monodomain liquid crystal elastomer. This switching is most dramatic when the strain is applied normal, or nearly normal to the initial director as a sharp jump of 90 degrees in orientation is seen. This molecular rearrangement is accompanied by a decrease in orientation parameter, < P-2 >, during the rotation. Wide-angle x-ray scattering (WAXS) and optical microscopy studies have revealed a single director orientation throughout the switching process; broad optical-texture variations are observed after the director flip has occurred, although the sample remains optically clear throughout the process.