Use of ultrasonic waves is continuously increasing for nondestructive evaluation (NDE) and structural health monitoring (SHM) in civil, aerospace, electrical, mechanical and bioengineering applications. Between bulk waves and guided waves, the latter is becoming more popular for NDE/SHM applications because the guided waves can propagate long distances and reach difficult to access regions. Recent advances in the research related to nondestructive testing (NDT) of composites and metals are discussed in this paper. To analyze the experimental results one often needs to understand the mechanics of wave propagation in various structures. Unfortunately, only for simple structures, such as homogeneous and layered half-spaces, plates, rods and pipes, the analytical solutions are available. Complex structural geometries with internal defects are difficult to solve analytically or numerically by the popular finite element method because at high frequencies the size of the finite elements becomes prohibitively small. An alternative mesh-free technique called the distributed point source method (DPSM) is being developed for solving such problems and is discussed here in addition to the experimental results.