Using the SIN and 2DE computer codes, we have conducted a numerical study of the shock initiation response of both bare and covered composition-B charges to projectile impact. In the bare charge case we observed two modes of shock initiation. Independence of the explosive response with respect to projectile aspect ratio was verified and critical conditions were determined as a function of projectile diameter with unit aspect ratio. The critical velocity was observed to have a linear dependence on the reciprocal of the square root of the diameter with values a little below experimental data. Additional linear relations to completely describe buildup to detonation were generated from the results. We found that development of detonation is similar in the case of covered charges. When the critical velocity was corrected for cover plate thickness, good agreement between the results for bare and covered charges was observed.