This paper proposes a new method to estimate failure strength of a pipe with local wall thinning. The method is based on the equivalent stress averaged over the minimum ligament in the locally wall thinned region. The highlight of the proposed method is to propose a simple scheme to estimate the equivalent stress in the minimum ligament. Inspired by the reference stress method for approximate creep stress analysis, approximate estimation equations are proposed for the equivalent stress in the minimum ligament, which are then calibrated using detailed elastic-plastic three-dimensional FE analysis. Remarkably the resulting estimation equations are found to be insensitive not only to pipe and defect geometries but also to material. Comparison of failure loads, predicted according to the proposed method, with published test data for corroded pipes shows excellent agreement, which provides confidence in the use of the proposed method to assess local wall thinning in pipes. Furthermore, the proposed method is conceptually simple and thus easy to be extended to more complex situations.