A method of numerical computation is presented in order to obtain equilibrium configurations in axisymmetric tori with ideally conductive shells of arbitrary cross-sections and/or with control-field coils. In this method, an artificial function S(ψ) is introduced, which makes it possible to combine the equilibrium equations in the plasma and the equation for the vacuum into one equation. The alternating-direction implicit method coupled with the Marder-Weitzner iteration scheme is used to solve the combined equilibrium equation under the boundary condition given on the shell. The continuity conditions at the plasma-vacuum interface are automatically satisfied in the solutions obtained. Some results of the computation are illustrated for cases where the shell shapes are of circular, square, rectangular and finger-ring type, respectively, and for a case with a ring coil placed inside the square shell.