Advances in recent 30 years in the theories of watershed runoff generation, flood wave movement in rivers, and watershed flow concentration are briefly introduced.

Also, flood wave disasters due to two kind explosions are discussed and great meaning of protection engineering for flood wave are described.

Based on the theory of 2-dimensional uniform stream,it gives characters of time and space involution of flood waves.

In this Dissertation, dam-break flood wave and the focusing of underwater shock wave in ESWL (Extracorporeal Shock Wave Lithotripsy) where the underwater shock wave is the most successful medical application are studied by using a novel numerical scheme (space-time Conservation Element and Solution Element method).