Numerical simulations are conducted to examine the effect of randomness in the bubble packing on the local elastic properties of a foam. We find that the response to a small-amplitude strain is spatially inhomogeneous : there are regions (of several bubbles) where bubbles shift their positions in order to prevent distortion. These regions respond differently when sheared in different directions, showing that the regions are elastically anisotropic. This work verifies assumptions made in an earlier, coarse-grained model.