Constraining the spatial variability of the thickness of the ice shell of Enceladus (i.e., the crust) is central to our understanding of its thermodynamics and habitability. In this study, we develop a new methodology to infer regional variations in crustal thickness using measurements of tidally-driven elastic strain. As proof of concept, we recover thickness variations from synthetic finite-element models of the crust subjected to diurnal eccentricity tides. We demonstrate recovery of crustal thickness to within ~2 km of true values with < 0.2 km error over spherical harmonic degrees l ≤ 12 (corresponding to half-wavelengths ≥ 60 km). Our computed uncertainty is significantly smaller than the inherent ~10 km ambiguity associated with inferring variations in crustal thickness solely from gravity and topography measurements. We therefore conclude that measuring elastic strain provides a relatively robust approach for probing crustal structure at Enceladus.