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Some recent experimental studies with pre-notched bend specimens of 4340 steel under both static loading[A. T. Zehnder and A. J. Rosakis, J. appl. Mech. 57, 618-626 (1990)] and impact loading [A. T. Zehnder et al., Inr. J. Fracture 42, 209-230 (199011 have shown that considerable crack tunneling occurs in the interior of the specimens prior to gross fracture initiation on the free surfaces. The Iinal fracture of the side ligaments happens because of shear lip formation. The tunneled region is characterized by a Ilat fi6rou.r fracture surface. In this work, the above experiments are analyxed using a 2D plane-strain finite-element procedure which is expected to simulate local material failure in the center-plane of the 3D specimen accurately. The rate-independent version of the Gurson model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage, and small particles which require large strains to nucleate voids. Attention is focused on the formation of a discrete void around a simulated inclusion ahead of the notch-tip, its growth and link-up with the notch-tip via a sheet of microvoids. In Part I of the work, the results obtained from the finite-element analysis of the static fracture initiation test [A. T. Zehnder and A. J. Rosakis, J. appl. Mech. !J7,618-626 (199011 are presented. It is found that the value of the J-integral at which material failure near the notch-tip commences in the present simulation agrees well with experimental observations regarding the onset of crack tunneling. The analysis of the impact fracture test of [A. T. Zehnder et al., Inf. J. Fracture 42, 209-230 (1990)] will be taken up in Part II.