This report documents practical modeling procedures adopted in the bridge engineering community involving seismic dsigns and retrofits of long span bridges relative to treatment of wave propagation problems. It also discusses wave scattering issues arising from irregular foundation boundaries affecting seismic loading of the bridges, which is not explicitly considered in th current design practice. Wave scattering is generally implemented in the nuclear power plant industry for seismic designs of various containment systems often using frequency domain computer programs. To examine the subject of wave scattering for application to long span bridge foundations, systematic modeling is exercised using a time domain based computer program and verification is made against a frequency domain computer program. For present day seismic designs of major bridges, nonlinear time history analysis is a common procedure to examine seismic loading of the structure permitting plastic hinging and ductility to be implemented. Thus, the current trend is to adopt time domain based computer programs for performing wave scattering analyses which can also serve as a common platform to be used by both geotechnical and structural engineers for the global bridge model. A major benefit is to minimize the amount of work for data transfer and potential error arising from two different groups (geotechnical and structural engineers) working on different computer codes requiring different input/output. By using the same computer code by both geotechnical and structural engineers, many problems are eliminated. Typically, wave scattering analyses are conducted in the frequency domain. This report presents studies of wave scattering using a time domain computer program. The same computer program can be used by structural engineers to proceed with coding the superstructure model, directly using the results from the wave scatterings analysis. The report presents various sensitivity analyses in order to minimize wave reflection and refraction at the model's side boundaries. Numerical integration schemes and implementation of Rayleigh parameters are discussed. Careful examination of waves traveling the bottom boundary allows proper modeling of the half-space below the region of interest. The studies explore the effects from wave scattering on large pile groups and soft ground conditions, and findings on the frequency ranges where significant scattering is observed are reported. Large caissons are know to affect seismic wave scattering due to the large wave length implied by the dimensions of the foundation embedded in soil. Parametric studies are performed to examine the shaking level that is altered by the wave scattering mechanism. From the current findings, it appears that the wave scattering tends to reduce the shaking level, especially in the high frequency range, and hence is beneficial to the bridge design