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We numerically demonstrate atomic Fabry-Perot resonances for a pulsed interacting Bose-Einstein condensate (BEC) source transmitting through double Gaussian barriers. These resonances are observable for an experimentally-feasible parameter choice, which we determined using a previously-developed analytical model for a plane matter-wave incident on a double rectangular barrier system. Through numerical simulations using the non-polynomial Schödinger equation-an effective one-dimensional Gross-Pitaevskii equation-we investigate the effect of atom number, scattering length, and BEC momentum width on the resonant transmission peaks. For [Formula: see text]Rb atomic sources with the current experimentally-achievable momentum width of [Formula: see text] [[Formula: see text]], we show that reasonably high contrast Fabry-Perot resonant transmission peaks can be observed using (a) non-interacting BECs, (b) interacting BECs of [Formula: see text] atoms with s-wave scattering lengths [Formula: see text] ([Formula: see text] is the Bohr radius), and (c) interacting BECs of [Formula: see text] atoms with [Formula: see text]. Our theoretical investigation impacts any future experimental realization of an atomic Fabry-Perot interferometer with an ultracold atomic source.