Early observations by the EUV Imaging Telescope (EIT) on the Solar and Heliospheric Observatory indicated that propagating diffuse wave fronts, now conventionally referred to as "EIT waves," can often be seen on the solar disk with a propagation velocity several times smaller than that of H Moreton waves. They are almost always associated with coronal mass ejections. We have previously confirmed the existence of such a wave phenomenon with numerical simulations, which indicate that there does exist a slower moving "wave" much behind the coronal counterpart of the H Moreton wave. Further observations have disclosed many new features of the EITwaves: the waves stop near the separatrix between active regions, sometimes they experience acceleration from the active region to the quiet region, and so on. Here we report onMHD simulations performed to demonstrate how the typical features of EITwaves can all be accounted for within our theoretical model, in which the EITwaves are thought to be formed by successive stretching or opening of closed field lines driven by an erupting flux rope. The relationship between EITwaves, H Moreton waves, and type II radio bursts is discussed, with an emphasis on reconciling the discrepancies among different views of the "EIT wave" phenomenon.