Understanding how cells migrate through confined environments is crucial for elucidating fundamental biological processes, including cancer invasion, immune surveillance, and tissue morphogenesis. The nucleus, as the largest and stiffest cellular organelle, often limits cellular deformability, making it a key factor in navigating narrow pores or highly constrained spaces. In this talk, I will present a novel geometric surface partial differential equation (GS-PDE) framework in which the cell plasma membrane and the nuclear envelope are modeled as evolving energetic closed surfaces governed by force-balance equations. To validate the model, we replicate a biophysical experiment using a microfluidic device that imposes compressive stresses on cells driven through narrow microchannels under a controlled pressure gradient. I will discuss the results of our parametric sensitivity analysis, which highlights the dominant influence of specific parameters, such as surface tension and confinement geometry, as key determinants of translocation efficiency. Finally, I will show how this framework, while tailored to a specific experimental setup for validation, provides a robust, flexible, and generalizable tool for investigating the broader interplay between cell mechanics and confinement, laying the groundwork for integrating more complex biochemical processes like active migration.