The extremely diverse surface of comet 67P/Churyumov–Gerasimenko contains a large number of depressions or craters of very different scales. Among the most prominent are two large roughly circular depressions, each with radii of several hundred meters. In this work a model for the formation of the depressions is proposed. It is based on the theory of the deformation of a thin circular elastic plate under its own weight. The plate covers a circular cavity with a given radius. The resilience of the plate diminishes over time as a result of its thinning which is itself a consequence of sublimation. When the stress limit is achieved, a gravitational collapse occurs: the plate cracks and the remnants fall into the cavity bottom. A formula that links the radius of the plate corresponding to collapse with the plate thickness has been derived. The formula was discussed for the large intervals of the values of parameters that characterize surface layers of cometary nuclei. It was found that the surface above large cavities collapses sooner than one of a similar thickness that covers a smaller cavity. So, if the collapse mechanism theory works, that larger depressions are therefore older than smaller ones.