Hydroxyapatite (HA) has been proposed as a candidate material for bone implants because of its similarity to the inorganic phase in bone. However, due to its lower mechanical properties compared to bone, it has not been used in load bearing bone implants. Inclusion of second phase reinforcements in HA such as carbon nanotubes (CNT) and graphene nanosheets is expected to significantly improve its mechanical properties. In this study, a computational framework that will improve the understanding of the mechanical behavior of graphene nanosheet and CNT-reinforced HA-nanocomposites is proposed. The variation of elastic modulus of HA-nanocomposites is assessed based on the nanofiller type, volume fraction, alignment, area, thickness, and aspect ratio using the finite element modeling. The results of the simulations show that graphene nanosheets are more effective in improving the elastic modulus of nanocomposites than CNTs at similar volume fractions. HA-nanocomposites reinforced by graphene nanosheets exhibit transversely isotropic material properties and provide the highest elastic modulus when aligned along a direction or randomly distributed in a plane, whereas CNTs provide the best reinforcement when aligned along an axis. Variation in graphene nanosheet area, thickness, aspect ratio, and carbon nanotube length have negligible effect on elastic modulus of the HA-nanocomposite. In addition, comparison between the finite element simulations and theoretical calculations show that clustering of nanoinclusions reduces the effectiveness of the reinforcement they provide. The simulation results and the computational framework presented in this study are expected to help in determining the best design and manufacturing parameters that can be adapted for developing HA-nanocomposite bone implant materials.