This paper describes a method for extending the capability of the contour method to allow for the measurement of spatially varying multi-axial residual stresses in prismatic, continuously-processed bodies. Currently, the contour method is used to determine a 2D map of the residual stress normal to a plane. This work uses an approach similar to the contour method to quantify multiple components of eigenstrain in continuously-processed bodies, which are used to calculate residual stress. The result of the measurement is an estimate of the full residual stress tensor at every point in the body. The methodology is presented and the accuracy is assessed for a representative test case using a numerical experiment. Finally, a measurement is performed on a thick laser peened plate of 316L stainless steel to show that the approach is valid under real experimental conditions.