A process for detecting totally or partially hidden faults, such as cracks, and bubbles and the like in an opaque medium, by using microwave radiation. Microwaves from a transmitting antenna are directed against the surface of the medium which is to be inspected, and microwave radiation reflected or back scattered from the medium is detected and analyzed. In order to maximize the signal to noise ratio, minimizing the detection of radiation reflected by the surfaces of the medium itself, at least one of the transmitting antenna and the receiving antenna is oriented at an oblique angle relative to the surface of the medium.