The shapes and sizes of linear and circular multiple-ring macromolecules in the framework of the Gaussian model have been numerically investigated in terms of shape factors, asphericity and prolateness factors and parameters, and shrinking factors. Simple analytic expressions for the eigenpolynomials of the Kirchhoff or architecture atrices for both linear and circular multi-rings in the limit of an infinitely large individual ring have been obtained via a new recursion method. It is found that for both types of multiple rings, shape asymmetry increases while size decreases as the number of rings increases, and that asphericity and prolateness parameters for a circular 99-ring macromolecule or a doubly stranded closed random walk have stronger dependence on dimensionality of the space in which the molecule is embedded than those of its linear counterpart.