One of the characteristics to be achieved by biomaterials is to have similarity to the host material. In cases of bone substitution, hydroxyapatite (HA) shows considerable similarities to human bone. However, it shows itself with low mechanical resistance, which in many cases makes it difficult to apply in areas subject to high mechanical stress. Carbon nanotubes (CNTs) have low density and strong covalent bonding between their atoms, which gives high mechanical resistance to the material. For this reason, the influence with the HA structure of single wall, pristine CNTs and functionalized with organic hydroxyl (-OH) and carboxyl (-COOH) clusters with functionalization concentrations of 5, 10, 15, 20 and 25% were studied by means of computational simulation. The software used to perform the calculations was GULP and the applied force field was DREIDING. The lattice dynamics revealed that pristine CNTs have a lower interaction with HA because of their high chemical stability. In contrast, the CNTs functionalized with -OH and -COOH interacted better with the HA matrix, indicating that the functionalization may be a factor that optimizes the interaction between these materials. The results of the Root Mean Square Deviation (RMSD), for all systems with functionalized CNTs, reach a stability around a point of equilibrium around 15ps, proving that the interactions are stable. The calculation of the Bulk modulus indicated that we can control the ability of this material to resist volume changes for a given applied pressure, modifying the amount of functionalization present in the CNTs. The functionalities of 20% of -OH and -COOH present greater difficulty in undergoing deformations (greater value of the Bulk module). On the other hand, the functionalizations of 15% of -OH and 5% of -COOH were the most vulnerable to deformation (lower value of the Bulk module). Finally, the Poisson ratio indicates that the theoretical model applied to the systems is reasonable since these coefficients were within the proposed theoretical range.