When the wavelength of the ultrasound being used to characterize a flaw is of the same order of magnitude as the flaw size, conventional low and high frequency scattering approximations fail. In this frequency range, called here the resonance region, numerical methods are necessary. Here we show that one such method, the Boundary Integral Equation (BIE) Method, is an effective tool for solving elastic wave scattering problems in the resonance region provided some important modifications are made in the method as used previously by other authors. To illustrate the BIE method, scattering from a cylindrical void in two-dimensions is considered. Comparisons are given with complimentary analytical and experimental results.