In light of the important recent synthesis of a stable tetrasilacyclobutadiene dianion compound by Sekiguchi and co-workers and the absence of theoretical studies, ab initio methods have been used to investigate this dianion and a number of related species. These theoretical methods predict multiple minima for each compound, and most minima contain folded and bicyclic silicon rings. For (Si4H4)(2-), (Si4H4)(2-)center dot 2Li(+), [Si-4(SiH3)(4)]2(-)center dot 2Li(+), [Si-4(SiH3)(4)](2-)center dot 2Na(+), and [Si-4(SiH3)(4)](2-)center dot 2K(+), respectively, the energetically lowest-lying structures are designated A-3 (C-2 nu symmetry), B-8 (C-1 symmetry), C-1 (C-2 symmetry), D-1 (C-2 symmetry), and E-1 (C-2h symmetry). None of these structures satisfies both the ring planarity and the cyclic bond equalization criteria of aromaticity. However, all of the representative NICS values of these lowest-lying structures are negative, indicating some aromatic character. Especially, structures C-1 and D-1 of C-2 symmetry effectively satisfy the criteria of aromaticity due to the slightly trapezoidal silicon rings, which are nearly planar with nearly equal bond lengths. SiH3 substitution for hydrogen in (Si4H4)(2-)center dot 2Li(+) significantly reduces the degree of aromaticity, as reflected in the substantially smaller NICS absolute values for [Si-4(SiH3)(4)](2-)center dot 2Li(+) than those of (Si4H4)(2-) and (Si4H4)(2-)center dot 2Li(+). The aromaticity is further weakened in [Si-4(SiH3)(4)](2-)center dot 2Na(+) and [Si-4(SiH3)(4)](2-)center dot 2K(+) by replacing lithium with the sodium and potassium cations.