The paper is focused on an untypical dished head as a thin-walled shell of revolution. The goal of the analysis is the elimination of the edge effect arising in the joint of the cylindrical shell with the dished head. The meridian of the head is a curve composed of a circular arc and a polynomial of the fifth degree. The stress state in the dished head is studied analytically and numerically with the use of finite element method (FEM). Moreover, the buckling problem of the head is analysed numerically to determine the bucking mode and buckling load for internal and external pressure.