Condition based monitoring of Thermal Protection Systems (TPS) is necessary for safe operations of space shuttles. In the current research Terahertz radiation (T-ray) has been used to detect mechanical and heat induced damages in TPS tiles. Voids and cracks inside the foam tile are denoted as mechanical damage while property changes due to long and short term exposures of tiles to high heat are denoted as heat induced damage.Ultrasonic waves cannot detect cracks and voids inside the tile because the tile material (silica foam) has high attenuation for ultrasonic energy. Instead, electromagnetic terahertz radiation can easily penetrate into the foam material and detect the internal voids although this electromagnetic radiation finds it difficult to detect delaminations between the foam tile and the substrate plate. Thus these two technologies are complementary to each other for TPS inspection.Ultrasonic and T-ray field modeling in free and mounted tiles with different types of mechanical and thermal damages has been the focus of this research. Shortcomings and limitations of FEM method in modeling 3D problems especially at high-frequencies has been discussed and a newly developed semi-analytical technique called Distributed Point Source Method (DPSM) has been used for this purpose.A FORTRAN code called DPSM3D has been developed to model both ultrasonic and electromagnetic problems using the conventional DPSM method. DPSM has been extended from ultrasonic applications to electromagnetic to model THz Gaussian beams, multilayered dielectrics and Gaussian beam-scatterer interaction problems. Since the conventional DPSM has some drawbacks, to overcome it two modification methods called G-DPSM and ESM have been proposed.The conventional DPSM in the past was only capable of solving time harmonic (frequency domain) problems. In this research DPSM has been extended to model DPSM transient problems. This modified technique has been denoted as t-DPSM.Using DPSM, scattering of focused ultrasonic fields by single and multiple cavities in fluid&solid media is studied. A comparison between the radiation forces generated by the ultrasonic energies reflected from two small cavities versus a single big cavity is also carried out.