Structure and function of the adherent cell depend in a crucial way on its microenvironment, including the stiffness of its substrate. It is often asserted that substrate thickness (as opposed to stiffness) plays a negligible role and therefore may be considered semi-infinite. This assertion has been recently challenged, but the characteristic length scale to consider in this regard is poorly understood. We show here that this characteristic length scale is the lateral cell size. As substrate thickness approaches the lateral dimension of the cell, the apparent stiffness of the substrate is amplified to levels much greater than the intrinsic stiffness of the substrate. This change in apparent stiffness is readily sensed by the cell, leading to changes in cell spreading area, stiffness, and contractile forces. In contrast to these responses that occur over the length of the cell, mechanosensing around an isolated point force is influenced greatly by intrinsic substrate stiffness but to a negligible extent by substrate thickness. We conclude that mechanosensing of substrate thickness is dominated in large part by traction forces spread over the lateral dimension of the cell.