This paper focuses on the radiation shielding, structural and specifically mechanical features of the Hydroxyapatite (HAP) bio-composites which can be used instead of the bone and tooth tissues in the human body via FLUKA Monte Carlo Code (FMCC), Phy-X: PSD software, and an analytical method. Since HAP bio-composites are so brittle, their use is limited instead of bone in the human body. This challenging issue persuaded the scientists and researchers to solve the problem by inserting various oxide or dioxide materials into HAP bio-composites. Thus, in this work, TiO2 and CeO(2 )with different ratios of x = 0, 3, 7.5, 10 wt.% and y = 0, 2, 6, 7.5 wt.% are inserted into HAP bio-composites and thus eight types of S (S1, S2, S3, and S4) and B (B1, B2, B3, and B4) samples are produced. Using Artificial Neural Network (ANN), this study predicts and demonstrates the system's behavior. Outcomes reveal that increasing the TiO(2 )and CeO2 concentrations in the (100-x) HAP + xTiO2 and (100-y) HAP + yCeO(2) bio-composites will improve the gamma photon shielding performance of the S and B samples. Furthermore, the photon and electron spatial maps for simulated geometries related to the S4 sample are extracted by the FLUKA Monte Carlo Code and are represented graphically. The produced electrons with the highest energy are monitored in lead volumes due to various interactions of gamma photons with lead shields. In addition, sharp peaks are reported for Z(eff )curves related to the B samples which may be due to the K-edge absorption of the Ce in HAP samples. The FLUKA results are in full agreement with the predicted targets via the ANN algorithm. Moreover, increasing the CeO2/TiO2 concentrations in HAP bio-composites will enhance the rigidity of the chosen S and B samples. The rising percentage of the mechanical moduli related to the S and B series vary between 30% and 90% which may be due to the relationship between the density of the selected HAP bio-composites and mechanical moduli.