The slip velocity effect at the wall interface becomes important when the Knudsen number is above 0.01. In most problems, the Maxwell slip model is used based on the Tangential Momentum Accommodation Coefficient (TMAC), a gas-wall couple constant. The original Maxwell slip theory is isotropic which is not suitable for strongly anisotropic surfaces. The present work presents a multi-scale analysis of the anisotropic slip phenomenon which comprises three stages: i) the ab-initio study of the gas-wall interaction potential ii) Molecular Dynamic (MD) computation of the isotropic/anisotropic TMAC coefficients on different surfaces iii) MD simulation of gas flows using an anisotropic surface model and comparison with the slip theory. The interaction between an Ar gas atom and a solid Pt fcc (111) slab is carried out using CRYSTAL 09 software and PBE functional for solids (PBEsol). The ab-initio based results including equilibrium distance and adsorption energy are in good agreement with empirical results in literature. The gas-wall potential is then decomposed to pair-wise potentials for Molecular Dynamics simulation. Next, the TMAC coefficients are computed using MD method with the pair-wise potential. The gas atoms are projected onto the solid slabs with different arriving angle and relative momentum changes are measured to determine the TMAC coefficients. Different types of surfaces are considered in this paper including perfectly smooth crystalline surface, randomly rough surfaces obtained from atom deposition simulations and, anisotropic surfaces with stripes. The phantom layer technique is used to maintain the bulk solid atoms at constant temperature allowing the study of the temperature effect. The orientation dependency of TMACs is computed and analyzed in comparison with isotropic/anisotropic scattering kernel models. Finally, we use MD method to simulate gas flows in nano channel. Instead of describing explicitly the solid atomic wall, an effective anisotropic gas wall collision mechanism with TMAC coefficients determined previously is adopted. A special MD wall boundary condition is proposed to mimic the mechanism. Both pressure and acceleration driven methods are used to simulate gas flows in slip and transitional regimes. In the former method, a constant gravity-like force is applied to the gas atoms. The latter method controls the kinetic pressure difference between the inlet and the outlet. Numerical results are then compared with analytical solutions issued from the anisotropic slip theory. It is shown that the extension of the Maxwell's model using two TMAC parameters can describe quite well the anistropic slip effect in the slip regime.