It is known that the interstellar medium has multi-phase nature due to radiate cooling and heating, and it is highly dynamic gas because of frequent supernovae. In this seminar, based on the results of recent MHD simulations, dynamical evolution of the ISM triggered by shock wave is discussed. I first review the evolution from diffuse warm atomic gas to HI clouds, and then molecular cloud formation and its evolution is discussed. In all its evolutionally processes, instabilities triggered by shock wave such as thermal instability and Richtmyer-Meshkov instability play important role. If I have time, influence of realistic multi-phase ISM structure on the cosmic-ray acceleration in supernova remnant is also discussed.