Explicit Finite-Difference method was used to obtain the solution of the system of the non-linear ordinary differential equations which obtained from the non-linear partial differential equations. These equations describe the two- dimensional flow of a MHD third-order Nano-fluid with heat and mass transfer in a circular cylindrical tube having two walls that are transversely displaced by an infinite, harmonic traveling wave of large wave length. Accordingly, the solutions of momentum, energy, concentration, and Nano-particles concentration equations were obtained. The numerical formula of the stream function, the velocity, the temperature, the concentration, and the Nano-particles distributions of the problem were illustrated graphically. Effects of some parameters of this problem such as, local nanoparticle Grashofnumber Br, local temperature Grashof number Gr, Darcy number Da, magnetic field parameter M, Eckert number Ec, Dufour number Nd, Brownian motion parameter Nb, Thermophoresis parameter Nt, Prandtl number Pr, radiation parameter Rn, Lewis number Le, Sort number Sr,and Chemical reaction parameter Rc on those formula were discussed. Also, an estimation of the global error for the numerical values of the solutions is calculated by using Zadunaisky technique.