The analysis of axisymmetrical thin shells has always been an important part of the theory of structures, and recently the problem of the cooling tower has aroused considerable interest for practical engineering reasons. Various solutions have been obtained, using either the finite difference or the finite element methods, with varying degrees of success. Amongst the latter, elements such as the TRIB 3c from the ASKA library and the axisymmetrical elements from the SABOR programme, with either a straight or a curved meridian line, have given reasonable displacements. But, by the nature of these elements, the stress distributions are discontinuous across element boundaries. Other existing elements, e.g. the arbitrarily curved triangular shell element SHEBA developed by Professor Argyris's team at the ISD in Stuttgart, are also suitable for the purpose and yield an excellent estimation of the stresses.