Using a one-dimensional MHD model and the shock fitting method (SFM) we discuss the propagation of flare-induced shocks and the associated wave structure downstream. It is shown that in the downstream region a rarefaction wave system forms, consisting of a fast rarefaction wave pair and a reverse slow rarefaction wave and an entropy wave-like structure sandwiched in between. It is also shown that the alternative method, the shock capturing method (SCM) cannot provide an acceptable description of the propagation in the interplanetary space.