The problem of the diffraction of normally indicent longitudinal and antiplane shear waves on a Griffith crack located in an infinite, isotropic elastic medium is considered. A Fredholm integral equation of the second kind is derived in each case for the determination of diffracted field. From the integral equation an asymptotic development of the solution is obtained which is valid for wavelength long compared to the crack length. For wavelengths comparable with the size of the crack the integral equation is solved numerically. The stress and the displacement fields in the vicinity of the crack as well as the radiation field at points far away from the crack are computed for a range of values of the frequency.