Various mechanical models of live amnioserosa cells during Drosophila melanogaster's dorsal closure are proposed. Such models account for specific biomechanical oscillating behaviors and depend on a different set of parameters. The identification of the parameters for each of the proposed models is accomplished according to a least-squares approach in such a way to best fit the cellular dynamics extracted from live images. For the purpose of comparison, the resulting models after identification are validated to allow for the selection of the most appropriate description of such a cell dynamics. The proposed methodology is general and it may be applied to other planar biological processes.