Crack diffraction in a transversely isotropic material is analyzed. The solution is given for the diffracted field generated by incidence of a plane time-harmonic wave on a semi-infinite crack located in a plane normal to the axis of symmetry of the material. The exact solution is obtained by Fourier integral methods and the Wiener-Hopf technique. The diffraction coefficients have been used in the context of the geometrical theory of diffraction to compute high-frequency scattering by a crack of finite length. Applications to scattering by delaminations in a medium of periodic layering have been considered for the case that the wavelength and the crack length are of the same order of magnitude, but both are much larger than the larger layer thickness.