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  1. The SABRE (Sodium-iodide with Active Background REjection) experiment is a new detector based on NaI(Tl) scintillating crystals for the dark matter detection through the annual modulation. With ultra-pure crystals and an active veto system, based on liquid scintillator surrounding the crystal array, SABRE will reach unprecedented low background and the highest sensitivity among the present NaI(Tl) experiments. Moreover SABRE will be the first dark matter search with twin detectors located in the North and South hemispheres, in Gran Sasso National Laboratories (LNGS), Italy, and Stawell Underground Laboratories (SUPL), Australia, respectively. The double location will help to quantify possible seasonal effects, and is a unique feature to identify a modulation of dark matter origins. SABRE is presently in the Proof-of-Principle (PoP) phase, with the goal to measure the crystal intrinsic and cosmogenic backgrounds of one 5 kg crystal and the active veto efficiency. We have performed a full geometry Monte Carlo simulation in order to evaluate the background contributions in the two distinct operation modes foreseen for the PoP: the potassium Measurement Mode (KMM) and the Dark Matter Measurement Mode (DMM), where the liquid scintillator detector is used in coincidence or anti-coincidence with the crystal, respectively. This paper presents the resultsmore »of a detailed background simulation and the expected sensitivity for the SABRE full scale experiment.« less