The ring-core technique is a stress relaxation-based method that is used to determine surface residual stresses in a material based on the linear elastic theory. However, material yielding that is due to ring creation on a highly stressed body would cause some errors. In this article, plasticity effects on high-level uniform residual stresses calculated by the ring-core technique were examined via a numerical analysis. The plasticity error owing to yielding was obtained by comparing the applied stress and the calculated stress derived from finite element (FE) simulation. Moreover, using the prepared FE model, the effects of various parameters, such as state of loading, ring geometry, and tangent modulus, were investigated. The results showed a maximum 30 % positive errors in the calculated residual stresses and the great impact of ring geometry on the plasticity error. Based on the results, the optimized ring diameter and depth for suitable precision were proposed.