This paper theoretically analyzes the electrooptic modulation characteristics of a Kerr medium under two transversely applied electric fields, and hence optical materials exhibiting dual transverse electrooptic Kerr effect are decided. The refractive index ellipsoid analyses demonstrate that the electrooptic phase retardation in some Kerr media is proportional to the square of the amplitude of applied electric field but independent of its direction; and the azimuth angles of the field-induced birefringent axes are only decided by the direction of the applied electric field and independent of its amplitude. This electrooptic modulation characteristic can be named as dual transverse electrooptic Kerr effect. Excluding optical materials exhibiting Pockels effect and electrogyratory effect, the crystals of cubic 432, m3m point groups and hexangular 6/mmm point group, and all the isotropic optical media exhibit dual transverse electrooptic Kerr effect. Transparent ceramic-glass with large Kerr constant has been reported in recent years, and it will accelerate the applications of dual transverse electrooptic Kerr effect in many fields of optical science and technology.