An enhanced model of strain-gradient crystal plasticity is used to study the deformation behaviour of b.c.c. single crystals of a β-Ti alloy under indentation. In this model, both incipient strain gradients, linked to a component’s surface-to-volume ratio, and strain gradients evolving in the course of deformation were characterised. The results of numerical simulations are in a good agreement with the obtained experimental data demonstrating an anisotropic nature of surface topographies around the indents performed in different crystallographic orientations. The influence of evolved strain gradients on the surface profile of indents is demonstrated.