This Bulletin provides the designer with a simple and approximate method of calculating maximum stresses due to internal pressure at cylinder intersections. Formulas are provided for calculating membrane and bending stresses in both the vessel and the nozzle. However, this Bulletin does not present any rules for design, but it is rather intended to be an aid in assessing the local structural integrity of the vessel. Cylinder-cylinder intersections are commonly encountered as nozzles in pressure vessels or branches in piping. WRC 107 and WRC 297 provide simple cookbook methods of calculating stresses at such intersections due to external loadings. This Bulletin has been prepared to provide the designer with a simple and approximate method of calculating maximum stresses due to internal pressure at cylinder intersections. Formulas are provided for calculating membrane and bending stresses in both the vessel and the nozzle. ASME B&PV Code, Section III and Section VIII, Division 2, contain rules for calculating "stress indices' which, in effect, are stress concentration factors at openings for fatigue analysis. But such indices are provided for a number of specific geometries only and are limited to a few points on the vessel. The methods of this Bulletin will allow a simple and fairly accurate calculation of stresses at cylinder intersections, for a wide range of geometric parameters. The design formulas proposed in this Bulletin are based on the results of a parametric study using the FAST2 (Revision 3) computer program.