The analysis of damping phenomena. that occur in many physics and engineering problems, reformulated in terms of boundary integral equations and solved via the boundary element method, is a novelty. In this context, we develop here an extension of the so-called energetic boundary element method. recently proposed in literature [1], for the numerical solution of damped waves propagation problems exterior to open arcs in the plane. Hard scattering analysis of 2D damped waves will be carried out directly in space-time domain. The presented numerical results confirm accuracy and stability of the proposed technique, already proved for the numerical treatment of undamped wave propagation problems in several dimensions [2, 3, 4] and for the 1D damped case [5, 6, 7].