An existing model, the Bergen code, is used to simulate the propagation of ultrasonic beams of finite amplitude, due to rectangular and square sources. It is found that the edges of the source give rise to peaks in the diffraction pattern at the fundamental frequency, which can cause the strongest shockwaves to form off-axis. These tend to be sharply bounded, causing rapid variation in heat deposition and streaming pressure across even an unfocused beam, and suppressing axial maxima in the pressure field.