Quickly developing computer techniques empower numerical simulations in materials science, which connect abstract theories and empirical experiments. Both deterministic molecular dynamics simulation and stochastic Monte Carlo simulation can employ various levels of theoretical models, from classical potential to the state-of-the-art ab initio method, for different simulation accuracies and needs. After the overview of a variety of methods used in this thesis, namely, classical potential, tight-binding (TB), semi-empirical, and density functional theory (DFT) methods, three following examples demonstrate how the computer-assisted simulations enable us to investigate and predict physical and chemical properties of the nano-materials. Mass diffusion through the graphene layer is the first example, where the DFT saddle point calculations are performed to identify the transition states of carbon absorption, addimer flipping over the graphene layer, and C2 molecule dissociation. In the second example on the cross-linked carbon nanotube bundles, tight-binding method is used for cross-link modeling and energetic stability analysis. Based on the semi-empirical molecular dynamics simulations of the tensile strength testing, a phenomenological model is proposed. After all the parameters are extracted from the quantum chemistry calculations, a series of canonical Monte-Carlo simulations are conducted to statistically analyze the mechanical properties of a nanotube bundle with thousands of cross-links. The last example on silicon nanowire demonstrates how various methods in different levels can be bridged by the energy decomposition in the energetic analysis. A novel electro-mechanical property of the pentagonal silicon nanowire is predicted by the electronic band structure calculations.