The study of Residual Stress is gaining more and more attention due to its importance in design for structural integrity. At present a lot of emphasis is placed on understanding the origins of mechanical failure that lie at the nano-/micron-scale. This leads to the evident need for evaluating residual stress distributions at increasingly smaller scales, and the search for modern tools capable of accomplishing this task. Prior state-of-the-art methodologies mostly required expensive and time-consuming sample preparation and examination processes to evaluate residual stress, e.g. the study of thin TEM lamellae. The recent advent of Focused Ion Beam methods opened up methods suitable for direct application at sample surface, yet allowing the observation and quantification of stress relief phenomena at the nano-scale. In the last decade, technical aspects of FIB-based method(s) have seen significant development. On the other hand, the calculation framework employed to analyse the experimental outcome remained largely conventional, in most inconvenient for high precision analysis of challenging problems. In the present paper, the eigenstrain-based method previously presented by the authors for the depthresolved evaluation of equi-biaxial residual stress, is generalised to non-equi-biaxial distributions of residual stress. This extends the applicability of the method to a much wider class of problems. The use of cylindrical ring-core shape in FIB-DIC analysis allows reconstructing the full in-plane residual stress tensor as a function of milling depth. We report formulae for calibrated influence functions that have very broad applicability, and can be used in the overwhelming majority of cases. Their derivation is based on an extensive set of FEM simulations that allowed reliable identification of the limitations of this approach, and highlight the importance of making appropriate selection of ring-core diameter(s). Finally, experimental validation of the method is presented that involves the reconstruction a known non-equibiaxial residual stress depth profile, confirming the validity and reliability of the present approach.