The reliable mechanical functioning of small devices depends critically on our ability to control plastic flow in applications. The single-crystal pillar compression tests have recently taken over as the standard method for analyzing mechanical response at the nano and microscales [1]. These tests indisputably demonstrate a size-dependant mechanical response with detectable stress drops or strain bursts and localized deformation compromising the materials structural stability, i.e.ductile rupture. These findings represent a fresh obstacle for the continuum theories of crystal plasticity. Physically speaking, because of the intricate interactions between dislocations at the lattice scale, the total mechanical response of the resulting pillars varies on the size and shape rendering a continuum description challenging. In this work, we use an Eulerian crystal plasticity model based on a dislocation-density hardening law. Eulerian rate-dependent single crystal models are particularly suitable for solving boundary-value problems involving large strains and strain rates. They are able to describe both the lattice rotations and the rate-dependent plastic flow. To handle the non-differentiability of the plastic terms an iterative decomposition/coordination formulation coupled with the augmented Lagrangian method was used for the numerical intergration. Since the initial dislocation density is size-dependent, the simulation results based on our model indicate a size-dependent mechanical response of monocrystal pillars. This dependence is due to the initial dislocation density which is much larger for pillars size less than one micrometer. The qualitative description of micro-pillars response given by our numerical model confirmes the experimental results available in the literature [2]. [1] O.U. S and Ioan R. Ionescu, Tempering the mechanical response of FCC micro pillars: an Eulerian plasticity approach, Mech. Res. Comm. 2021. [2] D.M. Dimiduk, M.D. Uchic, T.A. Parthasarathy, Size-affected single-slip behaviour of pure nickel microcrystals, Acta Materialia, Volume 53, Issue 15, 2005.