Difference of failure modes was studied by finite element analysis for elbows with local wall thinning area particularly at inner surface of intrados of the elbow. Longitudinal wall thinning length, minimum thickness were kept constant but circumferential wall thinning width was varied to get $90^{circ}$, $180^{circ}$ and $360^{circ}$ thinning width. Elastic-plastic analysis were carried out under the combined loading conditions of internal pressure and in-plane bending moment closing the elbow. Von Mises stress were obtained from the outer surface central surface location in intrados, extrados and crown parts in elbow. The results showed that the plastic deformation and failure started from the crown location when the thinning width small ($90{sim}180^{circ}$). However, plastic collapse started from the intrados location when the thinning width is approaching $360^{circ}C$. This should be reflected to assess structural integrity of elbows after wall thinning measurement is made.