In our previous work, solutions of the shallow shell equations have provided the basis for efficient computer calculation for a reinforced opening in a cylindrical vessel. However, solutions are restricted to smaller nozzles and openings (d/D≤0.5). In the present effort, an approach for the large opening has been developed which retains computational efficiency and minimum user time. The total solution can be divided into “high” harmonics around the intersection curve, which are obtained from asymptotic analysis, and particular solutions and low harmonics of self-equilibrating loads, which are obtained as “cut” solutions. By this, the vessel is considered to be cut along the portion of the circumference inside the intersection curve. Appropriate discontinuities of stress and displacement on the cut provide the necessary solutions. Results for a rigid nozzle with external loadings show good agreement with the previous shallow shell calculations for d/D≤0.5 with a substantial divergence for larger values of d/D. The behavior at the limit of d/D = 1 remains to be clarified.