Using higher-order terms of the Williams expansion is necessary for assessment of fracture behavior of quasi-brittle materials. Multi-parameter fracture mechanics enables more accurate determination of the stress/displacement field even in a larger distance from the crack tip, thus the extended zone with non-elastic behavior typical for this kind of material can be well described. The so-called over-deterministic method (ODM) seems to be a suitable tool for the higher-order terms coefficients calculation, but its utilization exhibits some limitations. Therefore, extensive analyses have been performed in order to summarize recommendations regarding the mesh sensitivity, boundary conditions influence, etc. List of pieces of advice and author’s experiences presented in the end of this work should contribute to more accurate and effective utilization of the ODM.