The objective of this study is to classify the geometry of wall-thinning defect that causes a circumferential crack in the pipe elbows subjected to internal pressure. For this objective, first of all a criterion to determine the occurrence of circumferential cracking at wall-thinned area was developed based on finite element simulation for burst tests of pipe elbow specimens that showed axial and circumferential cracking at wall-thinned area. In addition, parametric finite element analysis including various wall-thinning geometries, locations, and pipe geometries was conducted and the wall-thinning geometries that initiate circumferential crack were determined by applying the criterion to the results of parametric analysis. It showed that the circumferential crack occurs at wall-thinning defect, which has a deep, wide, and short geometry. Also, it is indicated that the pipe elbows with larger radius to thickness ratio are more susceptible to circumferential cracking at wall-thinned area.