This research is to investigate the behavior of elastic waves in porous media consisting of fluid and solid. A new methodology for describing the wave motion of a fluid saturated porous medium is developed with the establishment of a mathematical wave model. Dynamic equations in the form of displacements of the fluid and solid are derived for analyzing the elastic waves propagating in homogeneous and isotropic porous media, which are subjected to excitations of multiple energy sources. Solutions of the wave equation are developed on the basis of the moving-coordinate method. Employing the model provided in this project, the relative displacement between the fluid and solid of porous media can be quantified and the wave field can be determined with the given media and multiple energy sources. Numerical simulations of the waves propagating in the porous media with multiple energy sources are also performed for demonstrating the application of the mathematical model developed. This project is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), Petroleum Technology Research Centre (PTRC), and the Canada Foundation for Innovation (CFI).