An accurate analysis of nonlinear photonic crystal (PhC) based resonant cavities is carried out. The nonlinearity considered for this analysis is a third-order nonlinearity with media composed of Kerr-like dielectric materials with an instantaneous nonlinearity. The analysis is performed with a robust and accurate finite-volume time-domain (FVTD) technique that for the first time has been extended in order to simulate nonlinear material with a Kerr-like instantaneous nonlinearity. From the analysis, interesting properties are revealed from the exploit of nonlinear characteristics of the PhC-based resonant cavities, properties that can be usefully applied for the realisation of all-optical circuits and specifically for optical switches.