In this paper, the structural modeling and numerical analysis of the composite ellipsoidal pressure vessel head with nozzle are presented. A structural joint is considered as intersecting composite ellipsoidal and cylindrical shells. The finite element method and two-dimensional laminated shell theory are used. The features of the stress state and distribution of stress components in shells for ellipsoidal shell with radial central and noncentral nozzle under internal pressure loading are discussed. The results presented of parametric study show the effects of elastic properties of multilayered composite shells and nondimensional geometric parameters of shell intersection.