The response of the conventional scanning acoustic microscope (SAM) to anisotropic materials is theoretically investigated. For this purpose, the reflection coefficient of plane acoustic waves incident on a liquid-solid interface is numerically calculated for a general anisotropic solid oriented in any arbitrary direction. In general, the reflection coefficient depends on polar and azimuthal angles of incidence. For the case of a circularly symmetric acoustic microscope lens, a mean reflectance function can be defined that depends only on the polar angle. With this mean reflectance function, it is very easy to predict the anisotropic material response of the acoustic microscope. It is found that, under certain conditions, the amplitude response of the acoustic microscope can depend heavily on the orientation of the solid material under investigation. The amplitude of the acoustic microscope signal is influenced by the orientation of the material because there is a cancellation of acoustic rays reflected from the object surface at different azimuthal angles. This cancellation is revealed as a minimum in the mean reflectance function. It is shown by numerical simulation that the sensitivity to orientation can be increased by the use of a ring-shaped insonification at the back of the acoustic lens.