In this research, structural modeling and stress analysis of shell intersections made of composite materials are presented. Numerical approach for stress analysis of the intersecting composite shells is based on the finite element method using a modified mixed formulation and two-dimensional laminated shell theory. The features of the calculation algorithm and specialized computer program SAIS are considered. Results of the stress analysis obtained for models of composite ellipsoidal head with offset nozzle under in-plane moment and outof-plane moment loadings are discussed. Results of parametric study presented show the effects of specific properties of composite materials on the maximum stresses in shells.