In this paper the numerical simulation of the steady incompressible viscous flow in a no-slip channel is considered. A sequence of approximate nonlocal artificial boundary conditions on a given segment artificial boundary is derived by a system of linearized Navier–Stokes equations and spectral techniques. Then the original problem is reduced to a boundary value problem in a bounded computational domain. The numerical examples show that these artificial boundary conditions are very effective and are also more accurate than Dirichlet and Neumann boundary conditions, which are often used in the engineering literature.