Summary: Recent biological experiments [T. Lämmermann et al., “Rapid leukocyte migration by integrin-independent flowing and squeezing, Nature, London 453 (7191), 51–55 (2008; doi:10.1038/nature06887); A. Reversat et al., “Cellular locomotion using environmental topography”, ibid. 582 (7813), 582–585 (2020; doi:10.1038/s41586-020-2283-z); E. M. Balzer et al., “Physical confinement alters tumor cell adhesion and migration phenotypes”, FASEB J. 26, No. 10, 4045–4056 (2012; doi:10.1096/fj.12-211441)] have shown that certain types of cells are able to move in structured and confined environments even without the activation of focal adhesion. Focusing on this particular phenomenon and based on previous works [G. Jankowiak et al., Math. Models Methods Appl. Sci. 30, No. 3, 513–537 (2020; Zbl 1436.35225)], we derive a novel two-dimensional mechanical model, which relies on the following physical ingredients: the asymmetrical renewal of the actin cortex supporting the membrane, resulting in a backward flow of material; the mechanical description of the nuclear membrane and the inner nuclear material; the microtubule network guiding nucleus location; the contact interactions between the cell and the external environment. The resulting fourth order system of partial differential equations is then solved numerically to conduct a study of the qualitative effects of the model parameters, mainly those governing the mechanical properties of the nucleus and the geometry of the confining structure. Coherently with biological observations, we find that cells characterized by a stiff nucleus are unable to migrate in channels that can be crossed by cells with a softer nucleus. Regarding the geometry, cell velocity and ability to migrate are influenced by the width of the channel and the wavelength of the external structure. Even though still preliminary, these results may be potentially useful in determining the physical limit of cell migration in confined environments and in designing scaffolds for tissue engineering.