A possible solution to the dark matter problem postulates that dark particles can interact with Standard Model particles only through a new force mediated by a "portal". If the new force has a U(1) gauge structure, the "portal" is a massive photon-like vector particle, called dark photon or A′. The PADME experiment at the DAΦNE Beam-Test Facility (BTF) in Frascati is designed to detect dark photons produced in positron on fixed target annihilations decaying to dark matter (e+e-→γA′) by measuring the final state missing mass. The experiment will be composed of a thin active diamond target where a 550 MeV positron beam will impinge to produce e+e- annihilation events. The surviving beam will be deflected with a magnet while the photons produced in the annihilation will be measured by a calorimeter composed of BGO crystals. To reject the background from Bremsstrahlung gamma production, a set of segmented plastic scintillator vetoes will be used to detect positrons exiting the target with an energy lower than that of the beam, while a fast small angle calorimeter will be used to reject the e+e-→γγ(γ) background. To optimize the experimental layout in terms of signal acceptance and background rejection, the full layout of the experiment was modelled with the GEANT4 simulation package. In this paper we will describe the details of the simulation and report on the results obtained with the software.