The scattering of elastic waves by a rectangular crack in a half‐space of arbitrary anisotropy is considered. The scattering problem is formulated as a hypersingular integral equation for the crack‐opening‐displacement by means of the half‐space Green’s tensor, which is solved by expanding in a double series of Chebyshev functions. Models of transmitting and receiving transducers give a complete model of ultrasonic testing. A few numerical examples are given. © 2003 American Institute of Physics