Methods for detecting and monitoring changes in mechanical structures and in walls of pipes, vessels and storage tanks, using muitimode acoustic signal propagation and detection, are described. Acoustic signals having chosen amplitude-time-frequency characteristics excite multiple modes in the structure under investigation, are generated and received at a small number of accessible locations, such as the ends of pipes and the tops and bottoms of vessels and storage tanks, with the inspection region between transmit and receive transducers. Small mechanical changes lead to acoustic scattering and attenuation among the various modes, which are detectable as changes in received signal intensity. Such changes may include material loss, material conversion and material addition. Once the structure is characterized in a known condition, the present method may be used to monitor the structure at a later time to determine whether changes have taken place. Methods for effective temperature compensation are also described. In addition, various pipe geometries and complex pipe geometries involving elbows, flanges, and the like can be monitored.