In exploding foil initiator (EFI) system, ignition of explosive charges can be realized through high speed impact of small plastic film flyer onto explosive surface, after a flyer is sheared out of plastic film and accelerated due to pulsed electrical energy deposition into thin metallic bridge. In this theoretical study, a numerical modeling has been established in order to predict and closely investigate a series of complex phenomena in EFI system which include metallic bridge burst and plasma expansion by joule heating followed by flyer acceleration and explosive charge detonation. Present computational models for thermal behavior of vaporized metallic bridge and flyer acceleration are coupled with plasma properties and RLC circuit equation. When compared with experimental data for modeling verification, the present modeling predicts flyer velocity very well for wide range of charging voltage. The explosive detonation threshold by flyer impact is also predicted and discussed, while the ignition threshold characteristics from present modeling agree well with corresponding test results.