Ultrasound simulators relying on impulse response methods are faithful to the mechanisms of image formation from the underlying radio-frequency signals, but as a result tend to be relatively slow. At the other extreme are fast techniques, often motivated by the development of teaching and training simulators, which approximate the image formation processes rather than rigorously modeling the underlying physics. Previously, we have shown that transmit field distributions from linear phased-array transducers can be modeled accurately and efficiently using arrays of point sources. This approach is now extended to point sources/receivers, which allows for simulation of the transmit/receive fields, and thus the physical processes underlying ultrasound image formation. Field distributions and fast-time signals are shown to compare favorably to those obtained using the impulse response method. Doppler spectrogram and B-mode images derived from these signals also show excellent agreement with the results obtained using the impulse response method, but with a computational savings of nearly two orders of magnitude. Because of the inherent simplicity of our Fast and Mechanistic Ultrasound Simulation (FAMUS) approach, CPU parallelization was readily achieved, and further orders of magnitude speed improvements, and thus real-time performance, can be anticipated via extension to modern graphics processing units.