This work presents a finite element analysis of the indentation size effect (ISE) experimentally observed in tests performed at submicron scale. A 3D model of a conical rigid surface indenting on a Nb single crystal at different depths has been developed. The bcc Nb material has been characterized within a finite-strain framework through a crystal plasticity model incorporating strain-gradient hardening. The hardness evolution for different material orientations and for different initial dislocation densities has been studied. The numerical results are compared with predictions of existing analytical models and with experimental results. (C) 2013 Elsevier B.V. All rights reserved.