In atomic force acoustic microscopy (AFAM) the cantilever of an atomic force microscope is vibrated at ultrasonic frequencies while a sample surface is scanned with the sensor tip contacting the sample. As a consequence, the amplitude and phase of the cantilever vibration as well as the shift of the cantilever resonance frequencies contain information about local tip–sample contact stiffness and can be used as imaging quantities. An appropriate theoretical description of the transfer of ultrasound in an atomic force microscope enables the measurement of the local mechanical material parameters of the sample surface by evaluating experimental cantilever vibration spectra. In the experiments presented here, we examine the sensitivity of the technique using silicon single crystals. Furthermore, we show that the ferroelectric domains of lead zirconate–titanate ceramics can be imaged by AFAM and that local elastic constants of the sample surface can be determined quantitatively. The lateral resolution of the technique is given by the contact area formed by the sensor tip and the sample surface, which can have a diameter of <10 nm. Copyright © 2002 John Wiley & Sons, Ltd.