Using a one-dimensional MHD model and the shock fithng method (SFM), this paper discusses the propagation of flare-indutal shocks and the assodated wave structure downstream. It is shown that in the downstream region a rarefaction wave systo fonns, consishng of a fast rarefachon wave pair, and a reverse slow rarefaction wave and an entropy wave-like structure sandwiched in it. The same problem is also treated by the shock capturing method (SCM). It is concluded by comparison that the SCM cannot provide a reliable and a qualitahvely acceptible description of the propagation of flare-indued shocks in the interplanetary space, whereas the SFM seems to be the only prondsing choice.