The scattering of polarized harmonic shear waves by a sharp crack of finite length under antiplane strain is considered. Use is made of integral transforms, which reduce the problem to the evaluation of a system of coupled integral equations. Special emphasis is placed on obtaining the detailed structure of the crack-front stress and displacement fields, which control the instability behavior of cracks in brittle materials. While the dynamic stresses around the singular crack point are found to be qualitatively the same as those encountered under statical loading, they differ quantitatively in that the intensity of the dynamical stress field, which may be regarded as a measure of the force tending to cause crack propagation, depends on the incident wavelength. At certain wavelengths, this intensification is shown to be larger than the static case. The method of solution in this paper applies equally well to boundary value problems in electromagnetic and acoustic theory.