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Thus far axial resolution in elasticity imaging has been addressed only empirically. No clear analytical approaches have emerged because the estimator is nonlinear in the data, correlation functions are nonstationary, and system responses vary spatially. This paper describes a linear systems approach based on a small-strain impulse approximation that results in the derivation of a local impulse response (LIR) and local modulation transfer function (LMTF). Closed-form Solutions for strain LIR are available to provide new insights on the role of instrumentation and processing on axial strain resolution. Novel phantom measurements are generated to validate results. We found that the correlation window determines axial resolution in most practical situations, but that the the same system properties that determine B-mode resolution ultimately limit elasticity imaging.