The present thesis investigates the dynamical behavior of an elastic particle in the presence of deformable walls, with the aim of assessing how wall properties influence particle shape and spatial distribution. The configuration considered is a planar rectangular channel in which the particle is transported by a Couette flow, studied in the low Reynolds's number regime. The numerical approach is fully Eulerian: the incompressible Navier–Stokes equations are advanced on a fixed grid using a finite-volume method. Fluid-structure interaction is incorporated into the momentum balance through force terms that map the particle elastic response onto the Eulerian framework; the particle is modeled as hyperelastic capsule enclosing an incompressible Neo-Hookean bulk material.