In this study, the interactions of two effective derivatives of the methotrexate anticancer drug with Single-wall carbon nanotubes (SWNTs) and Boron nitride nanotubes (BNNTs) in the gas phase were investigated using the DFT calculations. Through the DFT method, the effects of different solvents on the interaction of methotrexate derivatives with SWNTs and BNNTs within the Onsager self-consistent reaction field (SCRF) model, as well as the effects of temperature on the stability of interactions between compounds in various solvents were studied. Thermodynamic parameters, Frontier Molecular Orbitals (FMOs) and Total Density of States (DOS) of the title compounds were also studied using theoretical calculations. Molecular properties of the structures such as the ionization potential (I), electron affinity (A), chemical hardness (η), electronic chemical potential (μ) and electrophilicity (ω) were investigated as well. SWNTs are more suitable carriers for L-MTX and BNNTs are more suitable carriers for L-FMTX. Also, the interaction of methotrexate derivatives with SWNTs and BNNTs was examined via Amber, Opls, Charmm and MM+ force fields through the molecular mechanic (MM) method. The calculations were carried out through the Monte Carlo simulation methods at different temperatures. The effects of gas phase and various solvent media with different dielectric constants (water, DMSO, methanol, ethanol, CH2Cl2 and DMF) on the interaction of methotrexate derivatives were investigated using the aforementioned force fields. The MM+ force field, which is an exclusive force field for calculations related to macromolecules, had the lowest amount of energy and featured the most stable form of connection for Methotrexate derivatives connected to SWNTs and BNNTs. The most significant finding is that with respect to both thermodynamic properties and conformer populations, the Monte Carlo and Molecular Mechanics-Quantum Mechanics results are in agreement.