EOS® is an innovative X-ray imaging system allowing the acquisition of two simultaneous images of a patient in the standing position, during the vertical scan of two orthogonal fan beams. This study aimed to compute organs radiation exposure to a patient, in the particular geometry of this system. Two different positions of the patient in the machine were studied, corresponding to postero-anterior plus left lateral projections (PA-LLAT) and antero-posterior plus right lateral projections (AP-RLAT). To achieve this goal, a Monte-Carlo simulation was developed based on a GATE environment. To model the physical properties of the patient, a computational phantom was produced based on computed tomography scan data of an anthropomorphic phantom. The simulations provided several organs doses, which were compared to previously published dose results measured with Thermo Luminescent Detectors (TLD) in the same conditions and with the same phantom. The simulation results showed a good agreement with measured doses at the TLD locations, for both AP-RLAT and PA-LLAT projections. This study also showed that the organ dose assessed only from a sample of locations, rather than considering the whole organ, introduced significant bias, depending on organs and projections.