Abstract The deformation and cross-streamline migration of an initially spherical neo-Hookean elastic particle suspended in confined shear flow of Newtonian and Giesekus viscoelastic fluids is studied through 3D arbitrary Lagrangian Eulerian finite element method numerical simulations. In both a Newtonian and a Giesekus liquid, when suspended in a symmetric position with respect to the walls of the flow cell, the particle deforms until reaching a steady ellipsoid-like shape, with a fixed orientation with respect to the flow direction. The dependences of such deformation and orientation on the flow strength, the geometric confinement, and the rheological properties of the suspending liquid are investigated. If the particle is initially closer to a wall of the channel than to the other, it also migrates transversally to the flow direction. In a Newtonian liquid, migration is always towards the center plane of the channel. In a Giesekus viscoelastic liquid, the migration direction depends on the competition between the elastic and the viscous forces arising in the suspending fluid; in a certain range of constitutive parameters, an ‘equilibrium vertical position’ in between the mid plane and the (upper/lower) wall of the channel is found, which acts as an attractor for particle migration.