Using an atomic force microscope (AFM) we confined a smectic-A liquid crystal (LC) between a flat glass plate and a 10-μm glass sphere attached to the free end of the AFM cantilever. Both surfaces were treated with a surfactant that induces normal alignment of the LC molecules. We measured the force F acting on the cantilever while varying the plate-sphere distance D with subnanometer precision. For D < 50 nm, the force was periodically oscillating and decayed as D was increased. Analyzing the force in the framework of a simple model of elastic deformation of the smectic layers, we have evaluated the undeformed layer thickness a(0) and compressibility modulus B. Compared to other techniques used to determine a(0) and B, AFM measurements are faster and require a much smaller amount (microliters) of LC. Moreover, they are based on purely mechanical deformations of the LC structure and do not require any static or radiative electromagnetic field.