We suggest that velocities in some tornadoes may achieve much higher Mach numbers than generally believed. Compressible large-eddy simulations of corner flow dynamics in a tornado indicate that there are no apparent physical barriers to transonic speeds occurring within small regions of real tornadoes. Such conditions appear most likely to occur for corner flows within the low-swirl regime, where locally intensified velocities in a relatively small region below a vortex breakdown allow Mach numbers to be more than 4 times greater than that at higher altitudes observable by Doppler radar. Even larger local levels of intensification in Mach numbers can occur during a sharp temporal overshoot in near-surface intensity that simulations indicate may occur during certain periods of a tornado’s evolution (see abstract by Lewellen and Lewellen). Although there have been speculations about very high wind speeds in some tornadoes in the past, all documented evidence based on photogrammetric, radar or damage track studies indicate wind speeds no greater than the maximum associated with an F5 tornado (142 m/sec). Further, transonic velocities would require extremely low pressures of less than half an atmosphere to coexist in the local region, much lower than any recorded observation. If transonic velocities do occur, the lack of direct observational evidence to date likely arises from the combination of the relatively small volume where the highest velocities are expected to occur, the fact that the largest Mach numbers are expected to be associated with vertical velocities less than a 100 meters off the surface, and that this region of intense velocities would likely be surrounded by a cloud of thick debris.