An ab initio quantum chemical study is presented on 6π-electron four-membered 1,3-X2Z2Y2Z′2 (X = P, S; Y = C, N, O, P, S; Z, Z′ = H, lone pair) rings. Stationary points on the potential energy surfaces were fully optimized within the symmetry constraints using SCF/6-31G* and MP2/6-31G* methods and characterized by calculating the harmonic vibrational frequencies of the normal modes. It is shown that besides experimentally known 6π-electron four-membered rings (S2N2, S42+) several 1,3-X2Z2Y2Z′2 rings possess a planar (aromatic) configuration. Alternatively, a distorted Cs structure or a puckered C2v structure with a trans-annular bond are found. The theoretical geometric parameters are in good agreement with available X-ray crystallographic data on a number of these compounds, their derivatives, or their complexes with transition metals. The preference for a planar, distorted, or puckered structure is rationalized in terms of 1,3-repulsive interactions and stabilizing deformations of the planar rings.