The quartic force field of cyclic C-4 has been computed using basis sets of spdf quality and augmented coupled cluster methods. The effect of core correlation and further basis set extension has been investigated. Vibrational energy levels have been obtained using perturbation theory and two different variational approaches. A severe Fermi resonance exists between the most intense vibration, nu(6), and nu(3) + nu(5) through an exceptionally large k(356) = -258.2 cm(-1); a large k(1356) = -54.8 cm(-1) causes significant higher-order anharmonicity, including a shift in nu(6) of +9 cm(-1). C-4 appears to be an excellent test case for methods for solving the vibrational Schrodinger equation, since perturbation theory breaks down even when the above resonances are accounted for. Our best estimate for nu(6), 1320 +/- 10 cm(-1), may suggest its assignment to a feature detected at 1284 cm(-1) in argon and 1302 cm(-1) in krypton matrix, but this would imply an unusually large matrix red shift in argon.