It is shown that the pseudo Jahn Teller effect (PJTE) in combination with ab initio calculations explains the origin of instability of the planar configuration of tetrafluorocyclobutadiene, C4F4, with respect to a puckered structure and square-to-rectangle distortion of the carbon ring, and rationalizes its difference from the planar-rectangular geometry of C4H4 and nonplanar (puckered) structure of Si4H4. The two types of instability and distortion of the high-symmetry D-4h configuration in these systems emerge from the PJT coupling of the ground B-2g state with the excited A(1g) term producing instability along the b(2g) coordinate (elongation of the carbon or silicon square ring), and with the excited E-g term resulting in e(g) (puckering) distortion. A rhombic distortion b(1g) of the ring is also possible due to the coupling between excited A(1g) and B-1g terms, For C4F4, ab initio calculations of the energy profiles allowed us to evaluate the PJTE constants and to show that the two instabilities, square-to-tetragonal b(2g) and puckering e(g) coexist, thus explaining the origin of the observed geometry of this system in the ground state. The preferred cis-trans (e(g) type) puckering in C4F4 versus trans trans puckering (b(2u) in Si4H4 follows from the differences in the energy gaps to their excited electronic E-g and A(1u) terms causing different PJTE in these two cases.