In recent years numerical investigations of tsunami wave propagation have been spurred by the magnitude 9.3 earthquake along the Andaman-Sumatra fault in December, 2004. Visualization of tsunami waves being modeled can yield a much better physical understanding about the manner of wave propagation over realistic seafloor bathymetries. In this paper we will review the basic physics of tsunami wave propagation and illustrate how these waves can be visualized with the Amira visualization package. We have employed both the linear and nonlinear versions of the shallow-water wave equation. We will give various examples illustrating how the files can be loaded by Amira, how the wave-heights of the tsunami waves can be portrayed and viewed with illumination from light sources and how movies can be used to facilitate physical understanding and give important information in the initial stages of wave generation from interaction with the ambient geological surroundings. We will show examples of tsunami waves being modeled in the South China Sea, Yellow Sea and southwest Pacific Ocean near the Solomon Islands. Visualization should be a part of any training program for teaching the public about the potential danger arising from tsunami waves. We propose that interactive visualization with a web-portal would be useful for understanding more complex tsunami wave behavior from solving the 3-D Navier-Stokes equation in the near field.