Predicting arrival times of interplanetary(IP)shocks at the near Earth space is an important ingredient of space weather forecasting because the passage of an IP shock at Earth will compress the magnetosphere and produce corresponding space weather effects. We first review current prediction models and their prediction's statistical experience. Then we show the Shock Propagation Models(SPMs)developed by us. The first version, i.e. SPM, was established by combining the analytical study for the propagation of the blastwave from a point source in amoving, steady-state, medium with variable density(Wei,1982;Wei and Dryer,1991)with the energy estimation method in the ISPM model(Smith and Dryer,1990,1995).
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