Correlations of level changes with topography demand an assessment of the effect of an irregular free boundary on surface deformation. This is examined through a plane strain elastic model with topography of small slope, subjected to a change in the far-field horizontal stress. To leading order, vertical surface displacements due to the topographic perturbation are proportional to the local relief. Elevation-dependent uplift results from a compressional change, and downdrop results from a tensional change. The model further predicts that the ratio of elevation change to elevation is proportional to and of the same order of magnitude as the regional strain. Horizontal strains are locally perturbed by topography as well, with the magnitude scaling with the local slope.. The predicted localization of level changes is very small in aseismic regions and cannot contribute significantly to measured correlations. A test case in southern California bears this out, with strains of order 10-6 accompanied by elevation change to elevation ratios of order 10-4. Releveling following the Nankaido-Tonankai earthquakes, which induced large coseismic and postseismic strains, reveals scattered examples of elevation-dependent level changes. However, when compared to modeled strains, the correlations are again at least an order of magnitude larger than the localization effect predicted by the elastic model. Although the topographic perturbation of vertical displacements appears to be unmeasurably small, local variations in horizontal strain or borehole dilatation across steep relief may be discernible with current technology.