The General Antiparticle Spectrometer (GAPS) is a novel approach for indirect dark matter searches that exploits cosmic antiparticles, especially antideuterons. The GAPS antideuteron measurement utilizes distinctive detection methods using atomic X-rays and charged particles from the decay of exotic atoms as well as the timing and stopping range of the incoming particle, which together provide excellent antideuteron identification. Prior to the future balloon experiment, an accelerator test and a prototype flight were successfully conducted in 2005 and 2012 respectively, in order to verify the GAPS detection concept. This paper describes how the sensitivity of GAPS to antideuterons was estimated using a Monte Carlo simulation along with the atomic cascade model and the Intra-Nuclear Cascade model. The sensitivity for the GAPS antideuteron search obtained using this method is 2.0 $times 10^{-6}$ [m$^{-2}$s$^{-1}$sr$^{-1}$(GeV/$n$)$^{-1}$] for the proposed long duration balloon program (LDB, 35 days $times$ 3 flights), indicating that GAPS has a strong potential to probe a wide variety of dark matter annihilation and decay models through antideuteron measurements. GAPS is proposed to fly from Antarctica in the austral summer of 2019-2020.
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