Abstract: The Cartesian grid method initially developed for computing inviscid flows is extended to viscous flow problems. In order to reduce the number of mesh points and to be compatible with the anisotropic nature of viscous flows, an anisotropic Cartesian grid method is proposed. The stability of a space-centered interior difference scheme and that of a finite-difference solid wall condition are studied for the Cartesian grid. It is found that the anisotropic Cartesian grid method can substantially reduce the number of grid points without jeopadizing the accuracy.