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Abstract The storage of fluids in the subsurface is critical for a broad spectrum of applications including managed aquifer recharge, storage of liquefied carbon dioxide and hydrogen, geothermal heat extraction and exploitation of hydrocarbon. It is surprising then, that there has been relatively little measurement of the vertical distribution of poroelastic storage in geologic formations as compared with permeability. We present experiments in which fluid was injected into an important regional aquifer and the depth‐dependent strain response measured using fiber optic distributed acoustic sensing. The formation expansion and contraction in response to fluid injection were several 100 nanostrain. Strain, and the implied storage distribution, was highly localized in specific strata and demonstrated complex, hydromechanical behavior. This new window into fluid‐geomechanical coupling undermines some typically use models and observations currently in practice, but provides potential for complete representation and prediction of fluid storage in the subsurface.