The inextensible cylindrical shell theory and lubrication theory combine into a model for the elastohydrodynamics of a rolling-imprint modality of nanoimprint lithography (NIL). Foil-bearing theory describes the formation of the lubrication gap due to relative motion between a tensioned substrate and a rigid, cylindrical surface. Reproduction of the results of foil-bearing theory for both stiff and perfectly flexible substrates validates this coupled model and reveals a highly predictable region of uniformity that provides low shear stress conditions ideal for UV-cure. These results show theoretical limitations that are used to construct an operating window for predicting rolling-mode NIL process feasibility.