Purpose: Melanoma at the choroid region is the most common primary cancer that affects the eye in adult patients. Concave ophthalmic applicators with 106 Ru/ 106 Rh beta sources are the more used for treatment of these eye lesions, mainly lesions with small and medium dimensions. The available treatment planning system for 106 Ru applicators is based on dose distributions on a homogeneous water sphere eye model, resulting in a lack of data in the literature of dose distributions in the eye radiosensitive structures, information that may be crucial to improve the treatment planning process, aiming the maintenance of visual acuity. Methods: The Monte Carlo code MCNPX was used to calculate the dose distribution in a complete mathematical model of the human eye containing a choroid melanoma; considering the eye actual dimensions and its various component structures, due to an ophthalmic brachytherapy treatment, using 106 Ru/ 106 Rh beta-ray sources. Two possibilities were analyzed; a simple water eye and a heterogeneous eye considering all its structures. Two concave applicators, CCA and CCB manufactured by BEBIG and a complete mathematical model of the human eye were modeled using the MCNPX code. Results and Conclusion: For both eye models, namely water model and heterogeneous model, mean dose values simulated for the same eye regions are, in general, very similar, excepting for regions very distant from the applicator, where mean dose values are very low, uncertainties are higher and relative differences may reach 20.4%. For the tumor base and the eye structures closest to the applicator, such as sclera, choroid and retina, the maximum difference observed was 4%, presenting the heterogeneous model higher mean dose values. For the other eye regions, the higher doses were obtained when the homogeneous water eye model is taken into consideration. Mean dose distributions determined for the homogeneous water eye model are similar to those obtained for the heterogeneous eye model, indicating that the homogeneous water eye model is a reasonable one. The determined isodose curves give a good visualization of dose distributions inside the eye structures, pointing out their most exposed volume.