The reflection and refraction at a fluid–solid interface of an acoustic beam, whose amplitude is Gaussian in cross section and which oscillates harmonically in time, is studied. The incident and scattered beams are constructed using the complex source‐point method. The incident beam is specularly reflected except at angles near one of the critical angles, of which the Rayleigh angle is the most important. Near this angle the beam excites both a leaky Rayleigh wave and a reflected beam, and the interference between these two disturbances produces the beam shifting noted by other workers. Surprisingly, a backward‐traveling leaky Rayleigh wave is also excited, although its amplitude is quite small. The incident beam, near normal incidence, is refracted into a compressional beam and a shear beam, both of whose amplitudes are Gaussian in cross section. Whereas the incident beam has a circularly shaped cross section, both transmitted beams have elliptically shaped cross sections. Moreover, the transmitted beams spread rapidly so that the compressional and shear beams always overlap. This rapid spreading limits the resolution of ultrasonic probes used to find cracks or other defects in a solid.