An analytical and experimental research program has been initiated at NASA Langley to investigate the strain response of panels under severe thermal and/or acoustic loads. The overall purpose of this program is to develop an analytical model that predicts the stresses and strains leading to sonic fatigue failure in advanced aircraft and aerospace structures. Previous experiments, analyses, and results of this program are reviewed. The analytical modeling refinements and their effects on the calculation of strain are discussed, considering the inclusion of in-plane motion at the panel boundary; the use of the multiterm, multimode Ritz method; and the introduction of transverse stiffness at the boundary. Finally, the findings of the analytical modeling investigation are summarized.