This paper presents a semi-analytical model of shear wave scattering by a viscoelastic elliptical structure embedded in a viscoelastic medium, and its application in the context of dynamic elastography imaging. The commonly used assumption of mechanical homogeneity in the inversion process is removed introducing a priori geometrical information to model physical interactions of plane shear waves with the confined mechanical heterogeneity. Theoretical results are first validated using the finite element method for various mechanical configurations and incidence angles. Secondly, an inverse problem is formulated to assess viscoelastic parameters of both the elliptic inclusion and its surrounding medium, and applied in vitro to characterize mechanical properties of agar–gelatin phantoms. The robustness of the proposed inversion method is then assessed under various noise conditions, biased geometrical parameters and compared to direct inversion, phase gradient and time-of-flight methods. The proposed elastometry method appears reliable in the context of estimating confined lesion viscoelastic parameters.