Cells that are in the late anaphase or telophase stages of cell division are vulnerable to damage by AC electric fields that have specific frequency and field strength characteristics. The selective destruction of rapidly dividing cells can therefore be accomplished by imposing an AC electric field in a target region for extended periods of time. Some of the cells that divide while the field is applied will be damaged, but the cells that do not divide will not be harmed. This selectively damages rapidly dividing cells like tumor cells, but does not harm normal cells that are not dividing. Since the vulnerability of the dividing cells is strongly related to the alignment between the long axis of the dividing cells and the lines of force of the electric field, improved results are obtained when the field is sequentially imposed in different directions. The field may also be rotated through 360.degree. by applying AC waveforms with different phases to the electrodes.