A thin elastic filament embedded in an elastic medium is subjected to a concentrated longitudinal load. For two-dimensional geometry and a relatively stiff filament the application of the load gives rise to a system of wedge-like and cylindrical waves. The dynamic shear stresses at the interface of the filament and the matrix, and in the region of the cylindrical waves are determined by means of Fourier transform techniques and Cagniard's method [2]. At the wave fronts of the wedge-like waves the jumps in the shear stresses are computed. Along the filament, the magnitudes of propagating discontinuities decrease exponentially. Along rays normal to the wave fronts of the wedge-like waves, the magnitudes of propagating discontinuities remain unchanged.