The inviscid stability of Long’s vortex, which is believed to model tornado‐like flows, is investigated using a finite‐difference method. Flows of this type are found to be generally unstable to small, short‐wave, helical disturbances, while no instabilities to axisymmetric modes have been found using this method. This instability provides a possible mechanism for the development of ’’suction vortices’’ in tornadoes.