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The interface between nano-scale films is of relevance in many critical applications. Specifically, recent technological advances in semiconductor industry that utilize silicon-on-insulator devices have given importance to the understanding of thermal transport across Si-SiO2 interface. Estimates of interfacial (Kapitza) resistance to the thermal transport across Si-SiO2 films do not appear to exist at the present time. In this paper, we develop and carryout reverse non-equilibrium molecular dynamics simulations by imposing known heat flux to determine the Kapitza resistance between Si-SiO2 thin films. For the Si-SiO2 interface, the average Kapitza resistance for a ~8 Å thick oxide layer system was 0.503 × 10-9 m2K/W and for a ~11.5 Å thick oxide layer system was 0.518 × 10-9 m2K/W. These values were of the same order of magnitude as the Kapitza resistance values determined from the acoustic mismatch model and the diffuse mismatch model for the Si-SiO2 interface.