We present a theoretical formalism and simulation results that allow the incorporation of the elastic contrast properties of tissues with simple geometries into the elastographic noise models developed previously. This analysis results in the computation of the elastographic contrast-to-noise ratio (CNRe). The CNRe in elastography is an important quantity that is related to the detectability of a lesion or inhomogeneity. In this paper, the upper bound on the elastographic CNRe is derived for both a one-dimensional (1-D) and 2-D analytic plane-strain tissue model. The CNRe in the elastogram depends on the contrast-transfer efficiency (CTE) for both the 1-D and 2-D geometries discussed in this paper. The 1-D model is used to characterize layered structures and the 2-D model is derived for circular inclusion within a background of uniform elasticity. A previously derived classical analytic solution of the elasticity equations, for a circular inclusion embedded in an infinite medium and subjected to a uniaxial compression, is used to compute the upper bound of the CNRe. Monte Carlo simulations illustrate the close correspondence between the theoretical and simulation results.