Finite sample thickness effects on material elasticity measurements made using an atomic force microscope have been calculated. The model includes an elastic layer on an elastic foundation and simulates sample indentation under an applied load. Rigid axisymmetric tips with conical, paraboloidal, and hyperboloidal profiles are considered. The results show that a common approach to estimating elastic moduli from force-displacement curves can lead to a significant error that depends on the units of measurement. A method to unambiguously estimate and correct this error is proposed. In addition, it is shown that elasticity estimates for monolayer thick samples using the force-modulation technique can contain a substantial, sample thickness-dependent error. Local thickness variations can result in misleading contrast in force-modulation images for samples that are several nanometers thick.