Debonded fibers influence the macro-mechanical behavior of fiber-reinforced composite materials. Debonded fibers contribute to the initiation and growth of cracks at the fiber/matrix interface. To examine such problems, the scattering of elastic SH-waves (problem of anti-plane strain) from debonded fibers is studied with a numerical method which can handle the mixed boundary conditions on the partially bonded fiber. A modification of the null field of T-matrix method is developed for this purpose. The modification is achieved by the introduction of a mathematical surface. The simultaneous solution of the integral representations of the field scattered by the mathematical surface and the actual fiber surface give rise to sufficient equations that permit solution of the debonded fiber problem. The scattering cross-section and the far field amplitude are calculated as a function of frequency, fiber properties and debonding area. This will be of interest in structural applications where such cross-sections can be used to compute the dynamical effective properties of damaged composites.