Existing design codes propose different methods for the analysis of the junction region of conical and toriconical shells (limit analysis, shake down analysis, Kellog design approach, area replacement method) submitted to internal pressure load. However, now it is possible to develop generally valid and very precise guidelines based on linear and nonlinear Finite-Elements-Analyses. A clear difference is made between design with respect to fatigue strength and design according to load carrying capacity criteria. A major advantage of the Finite-Elements-Method (FEM) is the opportunity of its adaptation to given design criteria such as a strain limit or a plastification limit. It is shown how design curves can be directly derived from the FE-analysis with respect to fatigue strength (stress concentration factors) and load carrying capacity (design factors for the calculation of a required wall thickness). The material behaviour in the plastic region is considered with and without strain hardening. Large deformation effects as geometric nonlinearities can be involved in the analysis. The method can easily be applied for the analysis of other pressure vessel components.