This paper proposes closed-form plastic limit load solutions for elbow with local wall thinning at extrados under internal pressure. This work was performed using 3-dimensional, small strain FE analyses based on elastic-perfectly plastic materials. The wide range of elbow and local wall thinning geometries are considered. For systematic analyses for effect of axial thinning extent on limit loads, two limiting cases are considered; a sufficiently long thinning, and the circumferential part-through surface crack. Then, the closed-form plastic limit load solutions for intermediate thinning are obtained by using result of two limiting cases. The effect of axial thinning extent for elbow on plastic limit load is highlighted by comparing with that for straight pipes. Although the proposed limit load solutions are developed for the case when local wall thinning exist in the center of elbow, it is also shown that they can be applied to the case when local wall thinning exists anywhere within elbow.