In this work, a simplified structural analysis of the main dome of San Francesco di Paola in Naples is performed by adopting both analytical and graphical approaches. The analytical process is based on the simplified membrane theory and the graphical methodology on the slicing technique. Both methods are used to determine the safety of the dome design under vertical and horizontal loads. We explore the effects of earthquakes by introducing horizontal forces proportional to the weight. Since the slicing technique does not consider the hoop compressive stresses building up in the upper part of the cap, the geometrical safety factor obtained by combining the analytical with the graphical method for the sole dome is lower than the one obtained with the analytical method. The estimate of the a=g factor for the dome-buttress structural system obtained with the graphical method is greater than the level accepted for the seismic area of Naples.