The mesh dependency of the cavity growth model due to Rice and Tracey has been overcome by integrating it over a process zone surrounding the crack tip. This integral represents a modified damage potential. The critical value of the integral for crack initiation in weld material has been determined from a welded CT specimen by comparing the computed J with the experimentally measured J -initiation value. This critical value is then employed in 8 and 12 in. welded pipes having different through-wall cracks at the centre to predict the crack initiation loads under four-point bending. Close agreement between the computed crack initiation loads and the experimentally measured values justifies the usefulness of the present modified damage potential.