This paper treats the ductile failure initiation in circumferentially-notched tension specimens and explores the local damage model that is able to represent the continuous degradation of the deforming material. With the aid of finite element calculations, the notched specimens have been simulated numerically and the whole strain-stress history for each geometry derived. This allows determination of the evolution of strain-stress fields until fracture occurs. Two damage models were evaluated: the Rice and Tracey cavity growth model and a model which combines the latter with the plastic strain work, to derive an intrinsic parameter called ‘damage work’. These models could predict the location where the crack will initiate as well as the crack initiation step which is reached for a relatively constant value of the critical damage.