In nuclear pressure vessels, multiple surface cracks are often found by regular inspection. In order to evaluate the integrity of the vessels, ASME B&PV Code Section XI provides the flaw combination rules; however, its accuracy has not been clarified yet. For the analyses of interacting multiple semi-elliptical surface cracks, in 1983 Nishioka and Atluri developed the Vijayakumar, Nishioka, and Atluri (VNA) solution-finite element alternating method which is highly accurate and cost effective. Using this highly accurate VNA-finite element alternating method, the case of extremely closely located two interacting coplanar cracks was analyzed. From the numerical results, it is found that the B&PV Code Section XI provides a conservative flaw combination rule. Therefore, the B&PV Code Section XI is precisely verified by modern and accurate computational technologies.