Surface‐wave methods are widely used in earth sciences and engineering for the geometric characterization of geological bodies and tectonic structures of the subsurface. These techniques exploit the dispersive nature of Rayleigh waves to indirectly estimate shear wave velocity profiles from surface‐wave measurements; however, they are limited to parallel‐layered geometries. To overcome such limitations, we present a new class of geometric inverse models for a full waveform inversion (FWI) based on the boundary element method (BEM). The proposed approach enables an effective identification of two dimensional (2D) subsurface geometries by directly estimating the shape of laterally varying interfaces from raw measurements. It thus aims at filling the gap between the standard simplistic parallel‐layered‐based inversion and that of more complex three‐dimensional (3D) geometries based on finite element methods (FEMs). Numerical tests on synthetic data unveil the effectiveness of the inverse algorithm, and its applicability to field measurements is finally presented.