When Earth-skimming tau neutrinos interact within the Earth, they generate upgoing tau leptons that can decay in the atmosphere, forming extensive air showers. The Beamforming Elevated Array for COsmic Neutrinos (BEACON) is a novel detector concept that utilizes a radio interferometer atop a mountain to search for the radio emission due to these extensive air showers. The prototype, located at the White Mountain Research Station in California, consists of 4 crossed-dipole antennas operating in the 30-80 MHz range and uses a directional interferometric trigger for reduced thresholds and background rejection. The prototype will first be used to detect down-going cosmic rays to validate the detector model. A Monte-Carlo simulation was developed to predict the acceptance of the prototype to cosmic rays, as well as the expected rate of detection. In this simulation, cosmic ray induced air showers with random properties are generated in an area around the prototype array. It is then determined if a given shower triggers the array using radio emission simulations from ZHAireS and antenna modelling from XFdtd. Here, we present the methodology and results of this simulation.