||In this thesis, we test the accuracy of viscous flow solver on unstructured meshes. The proposed gas-kinetic method is composed of two steps-an initial reconstruction step and a gas evolution step. In the initial reconstruction step, the flow variables inside each cell are replaced by linearly distributed functions. In the gas evolution step, a multidimensional gas-kinetic BGK scheme for the compressible Navier-Stokes equations is used to compute numerical fluxes at a cell interface. The BGK scheme is an accurate Navier-Stokes solver, which is valid not only for the viscous shear or boundary layer cases, but also in the construction of a Navier-Stokes shock structure. Numerical results of several test cases for steady compressible viscous flow are presented.