This paper reports on analytical as well as computer simulation of waves propagating in sandwich-type composite structures. Sandwich-type composites are being studied for use in NASA's new heavy lift launch vehicle, and flaw detection is crucial for safety and for failure prognostics. Theoretical analysis, as well as numerical modeling, is needed for benchmarking of available technologies for structural health monitoring (SHM) sensors and sensor systems. This benchmarking activity is important for answering the basic question of what minimum flaw size can be detected by the existing SHM based monitoring methods. Sandwich panels with foam, WebCore and honeycomb structures were considered for use in this study. Eigenmode frequency analysis and Frequency Response Analysis of the panels were made to understand fundamental properties of the panel physics and limitations that may affect the application of current SHM sensors and methods. An analytical study of the transient wave propagation is considered based on Mindlin plate theory. The mathematical model, accompanied by numerical simulations, shows that small size defects can be recognized but the frequency of waves should be sufficiently high. It is concluded that a combination of analytical results coupled with the high-fidelity simulations should make it possible to analyze experimental data and to predict the applicability of SHM methods for this type of structure.