The structure and ring-puckering properties of cyclobutane and its perdeuterated isotopomer are studied using high-level ab initio methods and complete basis set extrapolations. Calculations reveal significant coupling between the ring-puckering (theta) and CH2-rocking (alpha) motions, with equilibrium angles (theta(oq) = 29.59degrees and alpha(oq) = 5.67degrees) that are within the range of experimentally determined values. Our best estimate of the inversion barrier is 482 cm(-1), in excellent agreement with recent experimental determinations. Ring-inversion transition frequencies are evaluated from the eigenstates of the intrinsic reaction coordinate potentials for cyclobutane and cyclobutane-d(S). Natural bond orbital analysis shows that sigma(CC) - sigma(CH)* and sigma(CH) - sigma(CH)* hyperconjugative interactions are strengthened as cyclobutane puckers, thereby suggesting that inversion barriers in four-membered ring systems are a consequence of electronic delocalization rather than torsional strain.