This article provides an overview of static damage phenomena and the physical models utilized to identify damage using measured data. Static damage models provide an understanding of the underlying physics associated with damage, which is usually described in terms of boundary conditions, loading conditions, and material, geometric, electromagnetic, and thermodynamic properties. Examples that apply static damage models to examine changes due to damage in elastic waves in structural materials are discussed. Additionally, as a sample sensitivity analysis study, damage in metallic, orthotropic, and composite plates is modeled as variations in local geometry, stiffness, damping, and mass density using two‐dimensional and three‐dimensional wave propagation models based on the local interaction simulation approach (LISA).