The objective of this study is to develop a local failure criterion for a wall thinning defect of piping components. For this purpose, a series of tensile tests was performed using several types of simulated specimens with different stress states, including smooth round bar, notched round bar (five different notch radii), and grooved plate (three different groove radii). In addition, finite element (FE) simulations were performed on the simulated specimen tests and the results were compared with the test results. From the comparisons, the equivalent stress and strain corresponding to maximum load and final failure of notched specimens were proposed as failure criteria under tensile load. The criteria were verified by employing them to the estimation of failure of grooved plate specimens that simulate the wall thinning defect. It showed that the proposed criteria accurately estimate the maximum load and final failure of grooved plate specimen tests.