At the nanoscale, surface effect could cause atomistic structures a pre-stressed or pre-deformed state, which would consequently have a great dependence on their bulk mechanical properties. Besides, according to molecular mechanics [1,2], the effect of the non-bonding interactions among the atoms that are separated by equal or more than two bonds, say, van der Waals (vdW) forces, should be taken into account. Thus, the underlying objective of the study attempts to explore the extent of the surface effect and the in-layer vdW interactions on the mechanical properties of single/multi-walled carbon nanotubes(S/MWCNTs) with two different types of chiralities, including zigzag and armchair. To deal with the problem, an atomistic-continuum modeling (ACM) approach is introduced. The ACM is established by molecular dynamics (MD) simulation and equivalent continuum modeling (ECM). MD simulation is adopted to derive the initial equilibrium state of CNTs due to the surface effect, and the ECM is applied to calculate the mechanical properties of CNTs. The ECM is formulated based on the finite element (FE) approximations, which are composed of three-dimensional beam elements and one-dimensional non-linear spring elements. They basically represent the bonding and non-bonding interactions, respectively. The equivalent material constants of these two types of elements are derived from classical molecular mechanics and beam theory. The present results are also compared with those obtained from other simulations and experiments.