This paper proposes a new mathematical model for tsunami generation, propagation in real-time simulation and visualization. The model is so called SiTProS (Siam Tsunami Propagation Simulator). We deduce the shallow water wave equation, nonlinear wave equation and the continuity equation that must be satisfied when a wave encounters a discontinuity in the sea depth by selecting a computation grid from the Etopo2. A tsunami struck the shores of southern Thailand and along the Andaman coast on the December 26, 2004. The hardest-hit area of affected provinces is given based on the shoaling, refraction, diffraction and reflection phenomenon. The SiTProS can run for any given regional or global grid with a prescribed topographic dataset as Etopo2. The finite difference method is used to solve the equation. The SiTProS provides five different computing regions, which are Asia, Europe, Arab (Iran-Kenya), Africa, and Andaman. The SiTProS is designed for interactive simulation and user friendly.