Abstract: A method of non-destructively testing materials comprises directing an incident beam of ultrasonic waves onto the surface of a material and detecting the beam reflected by the surface, the angle of incidence and the wavelength of the ultrasonic waves being detected, and the critical angle of incidence at which the energy of the reflected beam passes through a minimum being determined for at least two different wavelengths. A curve is then prepared showing how the critical angle or a quantity dependent thereon varies with the wavelength or a quantity dependent thereon. Apparatus for carrying out the method comprises a goniometer for transmitting the incident ultrasonic beam and detecting the reflected beam, means for varying the angle of incidence of the beam, means for varying the wavelength of the waves, and means for determining the critical angles of incidence. The invention is applicable inter alia to the testing of tempered steel components.