Residual stresses can occur in many engineering components such as aircraft and aerospace. They can be caused by the forces and thermal gradient imposed during the forming process. Compressive stresses are sometimes purposely induced in near surface of materials by shot peening to help resist crack growth and fracture of components and to increase the working life under fatigue load. The knowledge of the magnitude and the distribution of the residual stresses, allows the engineer to optimize the forming operation and the materials choice. Theoretical elastic analyses to characterize the calibration coefficients developed under both plane stress conditions are proposed. These coefficients are used to link measured surface and/or subsurface strain to the residual stress. Three dimensional finite element analysis were developed and used to predict the magnitude and the direction of principal residual stresses in the depth of the material. The effect of sample geometry is studied of spherical samples on the calibration coefficient.