Hydrodynamic flow-based trapping techniques provide a controlled framework for studying soft particle dynamics under extensional flow conditions. Cross-slot microfluidic devices are widely used for generating planar extensional flows and confining particles near stagnation points [1]. In practice, these devices are typically fabricated with channel heights much smaller than their in-plane dimensions and therefore modelled using thin-gap (Hele–Shaw) approximations [2]. The Hele–Shaw approximation corresponds to a singular thin-gap limit in which out-of-plane velocity gradients and associated stress components are suppressed [3]. Although this approximation accurately captures planar velocity fields, it does not necessarily guarantee correct traction or deformation predictions once the channel height becomes comparable to particle length scales or to the magnitude of particle deformation. In this work, we investigate the deformation dynamics of a single elastic particle in a cross-slot geometry, with the aim of assessing the validity of the thin-gap assumption through a direct comparison of thin-gap and finite-gap configurations. The surrounding fluid is modelled by the incompressible Navier–Stokes equations, while the particle is described using an elastic solid formulation. The resulting fluid–structure interaction problem is solved using a fully coupled, monolithic finite-element approach based on an Arbitrary Lagrangian–Eulerian (ALE) framework, allowing for a consistent treatment of large deformations and the moving fluid–solid interface. Thin-gap and finite-gap configurations are compared under the same flow conditions, enabling a direct quantitative assessment of deformation metrics such as particle elongation, orientation, and steady-state shape. The comparison provides insight into how finite-gap effects influence particle deformation and highlights the limitations of depth-averaged modelling assumptions in microfluidic extensional flows. The present study also provides the foundation for future reduced-order modelling efforts aimed at enabling model predictive control of soft particle dynamics in microfluidic devices.