Swelling of elastic networks is manifested in different ways depending on the available number of degrees of freedom. In elastic films near a rigid substrate, swelling induces either a simple change in height or a more complex in-plane buckling instability. This difference is due to an elastic mismatch at the film-substrate interface and can be described using a single parameter such as film thickness, given a material of constant elasticity. Unlike polymer thinfilms, patterned polymer nanostructures are constrained equally in all three dimensions near the film-substrate interface. Here, we present results on the out-of-plane buckling instability observed recently in elastic nanostructures. We find that this instability is not a function of a single dimension, but depends strongly on both length-to-width and height-to-width aspect-ratios.