The present work reports mis-match limit loads for V-groove welded pipe for a circumferential crack using finite element (FE) analyses. In our previous paper , closed-form solutions of mis-match limit loads were proposed for idealized butt weld configuration as a function of the strength mis-match ratio with only one geometry-related slenderness parameter. To integrate the effect of groove angles on mismatch limit loads, the geometry-related slenderness parameter has to be modified by relevant geometric parameters including groove angle, crack depth and root opening based on plastic deformation patterns in theory of plasticity. Circumferential through-wall cracks are located at the centre of the weld considering two different groove angles (45°, 90°). With regards to loading conditions, axial (longitudinal) tension is applied for all cases. For the parent and weld metal, elastic-perfectly plastic materials are used to simulate under-matching and over-matching conditions in plasticity. The overall results from the proposed solutions agree well with FE results.