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Within the framework of the finite element method (FEM) and linear elastic fracture mechanics(LEFM), the development of a numerical tool for fatigue crack propagation computations is inprogress. The method uses a combination of hexahedral and tetrahedral elements in order to achieveaccurate singular FE-fields in the crack front neighborhood. The structured mesh at the crack frontallows easy postprocessing of the computed FE-fields. Stress intensity factors (SIFs) and subsequentlythe equivalent SIF are determined at integration points directly ahead of the crack front. The crackgrowth rate is calculated from the equivalent SIF adopting a suitable crack growth law.A brief description of the aims and underlying theory behind the approach is given. Results from ananalysis of a gas turbine engine component illustrate how geometrical singularities may influence thecrack growth rate and direction.