The paper presents the equilibrium finite element discretization of symmetrically loaded spherical flat shells. It is based on Castigliano principle. A new second-order equilibrium finite element is suggested, and the equilibrium and physical equations, obtained for it by using the Bubnov-Galiorkin method, are presented. A mathematical model for solving the problem of the elastic shell computation is created, based on the above equations. The method-ology is illustrated by a numerical example. The results are obtained, using a computer-aided program developed by the authors. The calculation results, obtained using the mesh of the elements of various density, show that the accuracy of the created element and the convergence of the results are high
