This research develops an innovative method (non-destructive technique) for estimating residual stresses in a solid body. The new method considers residual stress as constitutive information, the values of which are derived from an appropriate combination of theory and experiment and by selecting the upper and lower bounds from measured parameters. The research will investigate conditions where the displacement or stress field is free from residual stresses and will examine the elastodynamics of residually stressed bodies. Determining the residual stress is the key to assessing the integrity and serviceability of mechanical components and structural systems. Available destructive and non-destructive methods are not fully adequate to measure residual stress distributions in a solid body. The research will have a fundamental impact on the prediction of the integrity and performance of structural and mechanical components which use materials with varying degrees of ductility.