[en] Subbarrier photofission cross sections and the fission half-lives have been calculated for ²³⁸U in terms of a suitable double-hump fission barrier model. The competition due to the gamma deexcitation to the shape isomeric state in the second well (and its consequent fission) has been included by introducing an absorptive part in the potential in the second well region. The calculated cross sections reproduce satisfactorily the recently observed ''shelf'' in the deep-subbarrier energy region and result in a resonance structure in the threshold region consistent with that observed. The calculation also predicts several low energy resonances in the cross sections and a detailed competition of the prompt and the delayed fission contributions suggests that an angular anisotropy measurement might be more sensitive in detecting the relatively small contribution of delayed fission in the energy region 4.5--5.5 MeV