Propagation of an interplanetary (IP) shock through the bow shock and magnetosheath is studied using numerical results of a three-dimensional MHD model of the magnetosheath. According to already published theoretical studies, a fast forward shock passing through the bow shock would generate a train of new discontinuities including a slow expansion wave, a contact discontinuity, and a slow reversed shock. We have found that these particular discontinuities propagate with similar velocities and thus they cannot be distinguished in our calculations, and we observe one discontinuity that combines properties of all of them. We suggest that the same would be true for an analysis of experimental data. We have simulated three different ways of the magnetopause response to the IP shock. A comparison of these runs reveals that the magnetopause reaction defines the mode of reflected waves. Assuming a fast earthward motion of the magnetopause, about 240 km s⁻¹ or more, we obtain that a fast rarefaction wave would propagate from the magnetopause toward the bow shock, while a slower magnetopause motion would result in a fast reversed shock. On the other hand, the speed of the IP shock propagation does not depend on the magnetopause response, and all three model runs confirm a deceleration of the modeled IP shock front in the magnetosheath in course of its motion from the subsolar region to the magnetosheath flanks.