This work presents the numerical analysis of cylindrical pressure vessels, modeled using axisymmetric shells and plates elements under internal pressure loads. The numerical analysis considers surface joints for various surface thickness ratios, from thin (ratio between radius and thickness greater than 10) to thick (ratio between radius and thickness less than 5) shells. Element displacement fields of axisymmetric plane elements are used to evaluate the stress state at the surfaces junctions, and the obtained results are compared to simplified analytical solutions. It is concluded that analytical approximate results present an acceptable solution for a large range of plates to shells geometries up to moderately thick shells, whereas for thin shells the finite element solution is necessary to be considered in order to accurately verify the stresses at plate to shell junction. Numerical tests applying ANSYS program are presented to demonstrate the performance of linear axisymmetric analysis applying quadratic elements in comparison to the analytical solutions also evaluating the limitations of the analytical model in the region of the geometric discontinuity of the proposed model.