Through three-dimensional finite element modeling, it is demonstrated that the nanoindentation response of piezoelectric nano-islands is strongly dependent on the shape of the nano-island and the depth of indentation. For indentations that are relatively deep (i.e., greater than 5% of the height of the islands), the substrate's elastic and plastic properties have a strong influence on the indentation response of piezoelectric nano-islands with substrate plasticity resulting in a significant reduction in the mechanical and electrical indentation stiffness. The predictions of the finite element models compare well with experiments on nano-islands of strontium-doped lead zirconate titanate.