AbstractIn this work, the multi-parameter description of the crack-tip fields is employed. The Williams expansion is introduced for approximation of the stress/displacement distribution. The over-deterministic method is used for calculation of the coefficients of the power series terms because it requires only a conventional FE analysis. Particularly, the plastic zone extent in a cracked specimen subjected to I+II mixed mode of loading is investigated using Rankine criterion. Results determined via finite element analysis are compared to those calculated by means of the stress distribution expressed via the Williams expansion under consideration of various numbers of initial terms of the series. The size of the plastic zone is calculated for various values of tensile strength of the material modeled in the numerical simulations. It is shown that the higher-order terms of the Williams expansion can be significant when the extent of the nonlinear zone is large enough in comparison to the typical structural dimensions.