We present model calculations of high-order harmonic generation in benzene, aligned in the polarization plane of circular polarized laser field. The resonance states of the system are obtained using complex scaling Floquet approach (i.e., within non-Hermitian quantum mechanics) combined with (t,t(')) time propagation method. Our results show that the photo-induced dynamics of the model benzene molecule at the laser wavelength of 800 nm is dominated by a single long-lived resonance state up to the intensity of about 90 TW cm(-2). The high-order harmonics emitted by the system obey the selection rules derived in [Phys. Rev. Lett. 80, 3743 (1998)] on the basis of the dynamical symmetry of the system, namely the emitted harmonics possess the frequencies (6+/-1)omega,(12+/-1)omega,..., where omega is the incident laser frequency. These symmetry-allowed harmonics are found to be the dominant ones in the spectrum also when the laser polarization deviates from the "ideal" circular one by about 5%. The nonlinear response of the model benzene molecule is found to originate mainly from the field-induced transitions between the bound states, in accordance with the earlier analytical theory. The cut-off position in the calculated high-order harmonic generation spectra depends linearly on the field strength in the studied intensity interval. Our numerical calculations reveal the enhancements of particular high-order harmonics in the plateau region of the spectrum at certain field intensities. We show that these enhancements occur under conditions of avoided crossing of two or several resonance quasi-energies in the complex energy plane. (C) 2003 American Institute of Physics.