The present work is concerned whit critical stresses due to the combined affect of axial loads and intornal pressure in nossles welded to cilindrical pressure vessels whit conical hoads. The problem is treatod analytically through, axisimetric, thin ahell theory. The method of flexibility is employed to enforce the continuity of loads, moments, displacements and rotations at the junctions. A computer code has been developed for the calculation of the critical atresses in the nozzle, as well as the stresses resultants, moments, displacements, and the rotations along the atracture. It has been observed that for a griven configuration (nozzle and vessel diameters and angle of the conical head), there is an optimum between the nozzle and head thickness for which the stress concentration factor is minimum. This ratio is independent of the relation between the axial hoad and internal pressure.