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A quantitative sonoelastographic technique for skeletal muscle tissue characterization is introduced. Experimental data was collected in both ex vivo bovine and in vivo human skeletal muscle tissue. Crawling wave sonoelastographic data was processed using a quantitative technique for estimating local shear wave speed distributions. Results on ex vivo skeletal muscle samples demonstrate shear wave anisotropy and existence of fast and slow shear waves corresponding to propagation parallel and perpendicular to muscle fibers. Comparison of relative frequency-dependent changes between shear wave speed estimates for both shear wave propagation parallel and perpendicular to muscle fibers suggests increased viscoelastic effects for the former. Preliminary sonoelastographic data from two healthy human subjects was acquired in the relaxed rectus femoris muscles. Results demonstrate that quantitative elasticity data can be reproducibly acquired in vivo. Overall, preliminary results are encouraging and quantitative sonoelastography may prove clinically feasible for the in vivo characterization of skeletal muscle in health and disease.