We have reported results of nanoindentation using spherical indenters to observe the full indentation stress-strain curve. We observe the onset of plasticity in semiconductor strained-layer superlattices. These structures have alternating layers with strains of opposite sign. The yield pressure is reduced by the presence of the coherency strain. By varying the thicknesses and strains, we have been able to show that both sets of layers, compressive and tensile, reduce the yield pressure. This requires that a yield criterion must be satisfied over a volume, large enough to include layers of both sign. In these studies, we observe a large and reproducible size effect in the yield pressure. That is, with smaller radius indenters the mean pressure acting over the contact area at the deviation from purely elastic behaviour increases, by up to a factor of two for a 2μm radius indenter tip. Here we show how the requirement for meeting a yield criterion over a finite volume naturally leads to the size effect. Essentially, with smaller radius indenters, the peak stresses must be greater in order to satisfy the yield criterion over a finite volume. By integrating the strain energy over a suitable volume we show that there is a critical volume of ≍ 0.5μm radius over which yield is initiated for all indenter radii in the range 1-35μm. This is an important result for the understanding of nanoindentation and other systems in which stresses are highly inhomogeneous on a small scale.