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The boundary integral equation method is very often used to solve exterior problems of scattering of waves (elastic waves, acoustic waves, water waves and electromagnetic waves). It is known, however, that this method fails to provide a unique solution at the so-called irregular frequencies. This difficulty is inherent to the method used rather than the nature of the problem. In the context of elastodynamics, we proposed, in a recent work', two methods for eliminating these irregular frequencies. Both are based on modifying the fundamental solution. Here we present numerical results pertaining to the solutions of the modified and unmodified integral equations. I . INTRODUCTlONConsider a homogeneous isotropic elastic solid of unbounded extent, containing an infinite cylindrical cavity of smooth cross-section. Suppose that the cavity is irradiated by time-harmonic stress-waves, of frequency w, propagating perpendicular to the generators of the cylinder so that the material is in a state of plane strain. We wish to determine the scattered waves when the boundary of the cavity is free from applied tractions. This leads to a linear two-dimensional boundary-value problem in any plane perpendicular to the generators of the cylinder.Let D -denote the interior of the cylinder, with smooth boundary curve 6D. Let D denote the unbounded region outside i?D. Choose Cartesian co-ordinates (xl, x2) with origin 0 in D _ . We shall also use the following notation.Capital letters P, Q denote points of D; lower-case letters p , q denote points of dD; and P -, Q-denote points of D -; b(p) is the unit normal at p~6 D pointing into D; uinc and tinc are the incident displacement and stress, respectively.The decomposition of the total displacement u and thus of the total stress T in the form = ,,ino ' + ~S C and t = tint + TSC defines the scattered displacement us' and stress t P ' , respectively. Mathematically, the scattering boundary-value problem can be formulated as follows. Boundary-value problem S(uinc): determine a function us' for P E D , satisfying with k2 = pw2/(% + 2p) and K 2 = pw2/p, where p is the mass density of the solid and , i and 11 are the Lame constants.