As cells migrate within three-dimensional environments, they encounter a variety of physical barriers, including other cells, cell-cell junctions, and extracellular matrices (ECMs) of varying density and composition. This migration process often involves significant cell deformation, especially when the production of proteolytic enzymes is inhibited or when cells move through engineered scaffolds or microchannels. Experimental studies [1] have highlighted the existence of a critical ECM pore size below which cell migration is entirely impeded. Consequently, incorporating the microscopic mechanical properties of the cell—particularly those of the nucleus, the stiffest organelle—into mathematical models of cell migration is essential. Moreover, biological experiments [2] have shown that certain cell types are capable of migrating in structured and confined environments even in the absence of focal adhesion activation. Building on this observation, we develop a novel two-dimensional mechanical model [3] based on the following physical components: (i) asymmetric renewal of the actin cortex beneath the membrane, leading to a retrograde flow of material; (ii) a mechanical representation of both the nuclear envelope and the inner nuclear content; (iii) the microtubule network that guides nuclear positioning; and (iv) contact interactions between the cell and the external environment. The resulting fourth-order system of partial differential equations is solved numerically to analyze the qualitative effects of key model parameters, particularly those related to nuclear mechanics and the geometry of the confining structure. In agreement with biological evidence, we find that cells with a stiffer nucleus are unable to migrate through channels that are navigable by cells with more compliant nuclei. From a geometrical standpoint, both cell velocity and migratory ability are influenced by the channel width and the wavelength of the external topography. Although still preliminary, these results may contribute to identifying the physical limits of cell migration in confined environments and inform the design of scaffolds for tissue engineering applications.