Matter removal is necessary in order to measure the stress tensor at an interior point of a solid by means of X-ray diffraction. This induces stress redistribution so that the measured stress is different from the original residual stress. This paper addresses the problem of reconstructing the original stress field from the measurements. A method of solution is described for the reconstruction problem, which leads to explicit inversion formulae for the case of some simple geometries. Closed-form expressions are obtained for the two- and three-dimensional half-space. For bodies of arbitrary shape, a numerical algorithm is proposed.