We present material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities. The material criterion with a new nonlinear figure of merit suggests that Si, GaAs and even AlGaAs cannot be considered as the materials for resonator-enhanced Kerr nonlinear switch at 1.55 mu m (0.8 eV) of wavelength, due to the large free-carrier nonlinearity excited by two-photon or three-photon process. Insulators with wider band-gaps such as SiO2 and Si3N4 will be interesting materials to investigate for this purpose. (C) 2007 Elsevier Ltd. All rights reserved.