If cracks are detected in power plant pipes and the cracks are allowable, the plants can continue operating without the need for repair/replacement. The allowability of cracks is determined by means of allowable stresses, based on failure stresses. Failure bending stress at crack penetration is estimated by applying the Local Approach of Limit Load Criteria, which is based on the net-section stress approach. Using the stress at crack penetration, the allowable bending stress can be calculated for a pipe with a circumferential part-through crack. The allowable bending stress decreases with increasing crack depth and angle, as expected. However, the allowable bending stress can have one of three characters, depending on crack size: i) leak-before-break (LBB) and crack growth stability, ii) non-LBB and crack growth stability, and iii) non-LBB and crack growth instability. Character iii) represents a severe crack, and special attention needs to be paid to such a crack, even if it is allowable. Frequent non-destructive inspection and precise calculation of subcritical crack growth are recommended in order to prevent unexpected failure, especially for small-diameter thin-walled pipes. The boundaries of leak-before-break and crack growth stability can be successfully expressed by appropriate equations.