The aim of this study was to assess the efficiency of the local defect correction multi-grid method on solid mechanics test cases showing local singularities and derived from an industrial context. The levels of local refinement are automatically obtained recursively, using Zienkiewicz and Zhu's a posteriori error estimator. Choices of the prolongation operator, the refinement ratio and criterion are discussed in order to give the most satisfactory performances. Comparisons with an h-adaptive refinement method show the efficiency of the tool presented here, in terms of its accuracy and the memory space and processor time required.