The strength, deformation and buckling of a large engineering structure consisting of four ellipsoidal shells, two cylindrical shells with stiffening ribs and large holes, one conical shell and three pairs of large flanges under external pressure, self weight and heat sinks have been analysed by using two kinds of five different finite elements - four assumed displacement finite elements (shell element with curved surfaces, axisymmetric conical shell element with variable thickness, three dimensional eccentric beam element, axisymmetric solid revolutionary element) and an assumed stress hybrid element (a 3-dimensional special element developed by authors). The compatibility between different elements is enforced. The strength analyses of the top cover and the main vessel are described in the paper.